






























































































































































































































































































































































































































































































































































































































































































































































































































































































J 





















i 


' 


























. 

































' 


' 






■ 









































































\ 
























































































DEPARTMENT OF COMMERCE AND LABOR 

COAST AND GEODETIC SURVEY 

O. H. TITTIvC^IT3Sr 

STJPERINTENDE NT 


GEODESY 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION 
UPON THE INTENSITY OF GRAVITY 

(SECOND PAPER) 


BY 

WILLIAM BOWIE 

Inspector of G-eodetic Work and Cliief of tlie Computing Division 
Coast and Geodetic Survey 


SPECIAL PUBLICATION No. 12 



. WASHINGTON 

GOVERNMENT PRINTING OFFICE 
1912 




Monorraofc 







- - . ■ * > —- • . •• . ' . 

. 

- V v - - - 

* ' - > 




. : >>£ ■ u - - y.\ * .?v ... . . -v. 

- < — - - - - - - - ’ - N ■ -v _ ' ' 

•- TV • . . K _ . t - - ■ ’ * y 1 ■ 

. -A . ■ ' 'v- ~ - ... ■ r- 








ft-i' i — 


-■ 


.*■ r- 












- V - ' ” 


■ ' r rS . 

. 


-- - yy 




■: : V .. •••• 

- 

. 






• • -• _ . 

■ '-'V . - ; . 


\ -- x 

v, 1 








- 


- . i- 


X-. 




i§pH; ' z ' 

- x * 

■ 

♦ • - / .. - " . - ' 




-■ / V 




r L /■ , 










; -f~ 

\ >. - 


. r 


C - >' 






✓ 

_ ■ V; • 






y ; - ‘ 




y- 


. ' - ~ ■ - 3 »& ' - 




v, ' - - V-;.- 


c / ■■ 

; - • -- 

- / - • 4 ■ • Ik <■ 

x • W'.- 

"S»v - r . **->-« 

’• ' , - , 

' 

.*-• V . - - 




c 




. 

{ ■■ ■ ? 

./ 


‘v 7 




i f - ■ - 

-- . v. - ,- - _ . .<V. 

X ' . .-VV- • 

r-V-'. :■■ • - - 

■ - -v r. ^ v 

< ■ 

■ ' ? 





— -/ 

/. 




t*r 


x 

r' 


• y • v 

'> ■ 

• - - C; - 

•• . - 


‘ ^ 






' ' i 

- 


>'= • 


1 


-. 






- 

■sJC, 


V 

1 y ' c ■ 

___ 

y.. - / 

&X-. : • - 

- 1 


- ' < - 

• . •. . / . % . • . r- 

. 

-v. - 

. 




T'. , 


- f 

* - 

^ r 


. < 




i. 


2 


■ •- 










- - - ' ^ 

, 

- 

' - - . 

V * -• . -■ V -■ - ' -• ■ 

: , • 

- r ' - 






V: : T 




z'- y 




v . » 

- . - ~- 

" 








/ , 




. . - 






• • • * v- < ; 

V- , . ■:■■ - .. 

V v -- 't ■ • : 

■ 

- 

S 

- - ' 

. , 4 - - v 

y . - - . . ' , . - - .. 

'* y . ' 

y ■ - , 






■ 

- - 








. -- — ^ 


- , i: 








. * •- 








" jV -• 








. - 


'J 




o4 






. .. 

. 


' , 




3 - .. 

'■ , * ' - • , 


3 












■ ^ ^ 






- 


-*■ - 




‘ x ■. 




r 








-cJ’- 





K < 






X . - 




v • 


S' 








* ■ 

. -. - •: X '. ' : . : s - • ' y ■ ' ’ V - 

' '' • r .. v ~ ‘ 


?/-y£ . x . .. - 

K 

- 

■; "• - ■ 

$*:£ > v -^; ' y. . - . ' • 

y ■ : .:■-■/ - 





0 : • . -1 

\ 


Vv 




• - 










‘ ~ * ^ 

> r *?-' ’& ' - . x 

• V, . , J - 


* • -■ • ' 

- ■ ' 'I ■ * V . 

- • >- - k 

'S - ' - 


- 

-r *> - 


. "- - ' v 

' y . ■ • , . - „ . :> ; - ■ .-• .; 


- 


: Af 

■ A-i~. 






- - \rl 

I 


■' •=’" ■' > s 




' .- 

•A 












■ -V 


• ' 


> ■ 





















DEPARTMENT OF COMMERCE AND LABOR 

U.S. COAST AND GEODETIC SURVEY 

O. HI. TITTIMZ^I-T 1ST 

SUPERINTENDENT 


GEODESY 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION 
UPON THE INTENSITY OF GRAVITY 

(SECOND PAPER) 


BY 


WILLIAM BOWIE 

/ 

Inspector of Geodetic Work and. Chief of the Computing Division 
Coast and Geodetic Survey 


SPECIAL PUBLICATION No. 12 



WASHINGTON 

GOVERNMENT PRINTING OFFICE 
















* tit '5~ 

OCT 3 19*? 


















4 






















CONTESTS. 


Page. 

General statement. 5 

Isostasy defined... 6 

Principal facts for 124 stations in the United States...!_ 8 

Correction to Helmert’s formula of 1901. 1.0 

Comparison of apparent anomalies by the new and old methods... 11 

Discussion of errors. 13 

Possible relations of anomalies to topography. 13 

Graphical comparison of the three kinds of anomalies.. 17 

Relation between new-method anomalies and areas of erosion and deposition. 18 

Relation between the new-method anomalies and the geologic formations. 18 

New-method anomalies in agreement with deftections-of-the-vertical residuals. 21 

Regional versus local distribution of compensation. 22 

Percentage of completeness of compensation.... 22 

Depth of compensation. 23 

Alaska gravity stations. 23 

Flattening of the earth. 24 

Summary. 26 


3 




















ILLUSTRATIONS. 


1. Map showing location of gravity stations used in the investigation. In pocket 

2. Lines of equal anomaly for new method of reduction. In pocket 

3. Lines of equal anomaly for Bouguer method of reduction. In pocket 

4. Lines of equal anomaly for free-air method of reduction.. In pocket 

5. Illustration from Supplementary Investigation in 1909 of the Figure of the Earth and Isostasy, showing resid¬ 

uals of Solution H, all stations, with areas of excessive and defective density, and showing also all gravity 

stations with new-method anomalies. In pocket 

4 













/ 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION UPON THE 

INTENSITY OF GRAVITY. 


SECOND PAPER. 


By William Bowie, 

Inspector of Geodetic Work and Chief of the Computing Division, Coast and Geodetic Survey. 


GENERAL STATEMENT. 

In September, 1909, Mr. J. F. Hayford, then inspector of geodetic work, presented a paper 
to the International Geodetic Association at London which gave a preliminary report on the 
investigation made by him on the effect of topography and isostatic compensation upon the 
intensity of gravity. That report has appeared as pages 365-389 of volume 1 of the Report of 
the Sixteenth General Conference of the International Geodetic Association in 1909. Fifty-six 
gravity stations in the United States were used in that report. 

Before the final report of his investigation could be completed additional gravity stations 
were established in the United States by authority of the Superintendent, under the direction 
of the writer, as inspector of geodetic work, and in order that all available data might be used 
for the basis of the complete report 33 additional stations were added to the 56 stations, making 
89 in all. In the final report on the new method of reducing gravity observations Messrs. 
Hayford and Bowie worked together and appeared as coauthors. That report bears the title 
The Effect of Topography and Isostatic Compensation upon the Intensity of Gravity, Special 
Publication No. 10 of the Coast and Geodetic Survey, 1912. 

Still more gravity stations in the United States are now available, making 124 stations in 
all, and it has been decided that a supplementary investigation of the effect of topography and 
isostatic compensation upon the intensity of gravity should be made. This present paper is a 
report on the second investigation. These reports on the investigations of the effect of topog¬ 
raphy and isostatic compensation upon the intensity of gravity are very closely allied to and 
may be considered as supplementary to the two publications of the United States Coast and 
Geodetic Survey by Hayford, entitled The Figure of the Earth and Isostasy from Measure¬ 
ments in the United States, and A Supplementary Investigation in 1909 of the Figure of the 
Earth and Isostasy. In these two publications only deflections of the vertical were utilized. 

The writer wishes to express his appreciation of the valuable assistance rendered by those 
members of the computing division of the United States Coast and Geodetic Survey who were 
connected with this investigation, especially Miss S. Beall and Mr. C. H. Swick. 

Anyone wishing to have full information on the subjects treated here should use with this 
paper the report of the first investigation entitled Effect of Topography and Isostatic Compen¬ 
sation upon the Intensity of Gravity. In that publication are given the detailed description 
of the new methods of reducing the gravity stations, together with the reduction tables for 
obtaining the topographic correction and the correction for isostatic compensation, and the 
formulas by which the values in the tables were computed. 


5 





6 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


ISOSTASY DEFINED. 

It is desirable that the reader who is not already thoroughly familiar with the contents of 
Effect of Topography and Isostatic Compensation upon the Intensity of Gravity be given concise 
definitions of the terms and phrases used, and for that purpose portions of pages 6 and 7 of 
that publication are repeated here. 

If the earth were composed of homogeneous material, its figure of equilibrium, under the 
influence of gravitation 1 and its own rotation, would be an ellipsoid of revolution. 

The earth is composed of heterogeneous material which varies considerably in density. 
If tins heterogeneous material were so arranged that its density at any point depended simply 
upon the depth of that point below the surface, or, more accurately, if all the material lying 
at each equipotential surface (rotation considered) were of one density, a state of equilibrium 
would exist, and there would be no tendency toward a rearrangement of masses. The figure of 
the earth in this case would be a very close approximation to an ellipsoid of revolution. 

If the heterogeneous material composing the earth were not arranged in this manner at the 
outset, the stresses produced by gravity would tend to bring about such an arrangement; but 
as the material is not a perfect fluid, since it possesses considerable viscosity, at least near the 
surface, the rearrangement will be imperfect. In the partial rearrangement some stresses will 
still remain, different portions of the same horizontal stratum may have somewhat different 
densities, and the actual surface of the earth will be a slight departure from the ellipsoid of 
revolution in the sense that above each region of deficient density there will be a bulge or bump 
on the ellipsoid, and above each region of excessive density there will be a hollow, relatively 
speaking. The bumps on this supposed earth will be the mountains, the plateaus, the conti¬ 
nents, and the hollows will be the oceans. The excess of material represented by that portion 
of the continent which is above sea level will be compensated for by a defect of density in the 
underlying material. The continents will be floated, so to speak, because they are composed 
of relatively light material; and, similarly, the floor of the ocean will, on this supposed earth, 
be depressed because it is composed of unusually dense material. Tins particular condition of 
approximate equilibrium has been given the name “isostasy.” 

The adjustment of the material toward this condition, which is produced in nature by the 
stresses due to gravity, may be called the “isostatic adjustment.” 

The compensation of the excess of matter at the surface (continents) by the defect of 
density below, and of surface defect of matter (oceans) by excess of density below, may be 
called the “isostatic compensation.” 

Let the depth below sea level within which the isostatic compensation is complete be 
called the “depth of compensation.” At and below tins depth the condition as to stress of 
any element of mass is isostatic; that is, any element of mass is subject to equal pressures 
from all directions as if it were a portion of a perfect fluid. Above tins depth, on the other 
hand, each element of mass is subject in general to different pressures in different directions—- 
to stresses which tend to distort it and to move it. 

Consider the relations of the masses, densities, and volumes, above the depth of com¬ 
pensation, fixed by the preceding definition. The mass in any prismatic column which has 
for its base a unit area of the horizontal surface which lies at the depth of compensation, for 
its edges vertical lines (lines of gravity) and for its upper limit the actual irregular surface 
of the earth (or the sea surface, if the area in question is beneath the ocean), is the same as 
the mass in any other similar prismatic column having any other unit area of the same surface 
for its base. 

1 In this publication “gravity” is the term'used for the phenomenon of weight or of the acceleration of a body falling to the earth, and, at any 
place, it is the resultant of the earth’s attractive force, “gravitation,” and the centrifugal force due to the earth’s rotation. This distinction 
between the terms “gravity” and “gravitation” is not always clearly drawn. 

In general it will be found that throughout this publication the attraction (expressed in dynes) is dealt with directly by preference rather than 
its numerical equivalent, the acceleration (expressed in centimeters and seconds). This preference is due to the belief that thereby circumiocu 
tions are avoided and greater clearness secured in the conceptions. 




EFFECT OF TOPOGEAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


7 


The most unusual feature of the first investigation of the effect of topography and iso¬ 
static compensation upon the intensity of gravity is that all of the topography 1 of the world 
and its isostatic compensation are taken into consideration in computing the effect on gravity 
at a station. 

For the purpose of making the computations the earth’s crust is assumed to be in a state 
of perfect isostasy, with each topographic feature compensated for by a deficiency (or excess) 
of mass directly under it; and it is assumed that this compensating deficiency (or excess) of 
mass is uniformly distributed to a depth of 113.7 kilometers. This depth is-that resulting 
from the investigation of The Figure of the Earth and Isostasy from Measurements in the 
United States. This value has been used in the investigations of gravity and in the new 
method of reduction, including the computations of the reduction tables. The better value 
for the depth of compensation of 122.2 kilometers resulting from the Supplementary Investi¬ 
gation in 1909 of the Figure of the Earth and Isostasy was not available at the time the gravity 
investigations were begun. This slight difference between the adopted and the better value 
of the depth of compensation does not affect the anomalies materially, nor would a change to 
the other depth have varied in the slightest degree any of the conclusions drawn from the 
gravity investigations. 

The mean density of the solid portion of the earth’s surface is assumed to be 2.67, and 
the density of the ocean water is assumed to be 1.027. 

Agreeing with similar statements made in the two publications on the figure of the earth 
and isostasy and in the one on the investigation of gravity, the writer does not believe that 
any one of the assumptions stated above is exactly true. 

The average density, 2.67, is no doubt somewhat in error, and it is reasonably certain 
that there are many areas where the average densities of the surface materials are very differ¬ 
ent from this adopted mean density. The mean depth of compensation is probably not exactly 
113.7 kilometers, and at different portions of the earth’s crust the depth of compensation may 
be very much greater or less than 113.7 kilometers. It is probable that the deficiency (or 
excess) of mass under a topographic feature is not distributed with exact uniformity with 
respect to depth, and it is also probable that the isostatic compensation or deficiency (or 
excess) of mass is not located exactly under a topographic feature. It is believed, however, 
that the assumptions made in connection with the investigations are very close to the truth. 
The anomalies or differences between the observed gravity and the value computed by the 
new method give an idea of the inaccuracy of the assumptions made. It will be shown later 
that the anomalies result partly from errors in making the observations and computations, 
but mostly from an actual departure from the postulated conditions in the earth’s crust. After 
allowing for the errors of observations and computations the remaining anomalies are of such 
a size that they clearly indicate departures from the condition of perfect isostasy in the earth’s 
crust in the vicinity of the station. 

The writer sees no reason for modifying Mr. Hayford’s statement which appears on page 
169 of The Figure of the Earth and Isostasy from Measurements in the United States, and 
which is repeated on page 102 of Effect of Topography and Isostatic Compensation upon the 
Intensity of Gravity, which reads as follows: 

In the above statement that the separate topographic features of the continent are compensated, it is not intended 
to assert that every minute topographic feature, such, for example, as a hill covering a single square mile, is separately 
compensated. It is believed that the larger topographic features are compensated. It is an interesting and important 
problem for future study to determine the maximum size, in the horizontal sense, which a topographic feature may 
have and still not have beneath it an approximation to complete isostatic compensation. It is certain from the results 
of this investigation that the continent as a whole is closely compensated and that areas as large as States are also closely 
compensated. It is the writer’s belief that each area as large as one degree square is generally largely compensated. 
The writer predicts that future investigations will show that the maximum horizontal extent which a topographic 
feature may have and still escape compensation is between one square mile and one square degree. This prediction 
is based, in part, upon a consideration of the mechanics of the problem. 


1 By topography is meant that portion of the earth's crust above sea level and the defect of mass in the oceans. 



8 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


PRINCIPAL FACTS FOR 124 STATIONS IN THE UNITED STATES. 

There is a statement in Special Publication No. 10, which gives the names of the observers 
who established the 89 stations considered in that publication. The additional 35 stations used 
in this report were established as follows: Nos. 102, 103, and 106, by Assistant W. H. Burger 
in 1909; Nos. 90 to 100, by Assistant H. D. King in 1910 and 1911; and Nos. 101, 103, 104, 
105, and 107 to 124 (22 stations in all), by Assistant T. L. Warner in 1911. Station No. 103 was 
established by Mr. Burger in 1909, but was reoccupied for further observations by Mr. Warner 
in 1911. 

The gravity observations at each of the stations used in this investigations were made with 
the half-second pendulum apparatus. (See App. 5, Coast and Geodetic Survey Report for 1901, 
by G. R. Putnam.) The methods used by Mr. Putnam were described by him in Appendix 
1, Report for 1894. With only slight modifications these methods were employed by the 
other observers who used the half-second pendulums. A radical change was made in the 
method of determining the flexure of the pendulum case. Beginning with the observations in 
1909 the flexure was determined in terms of the wave length of light with an interferometer, as 
described by Mr. W. H. Burger in Appendix 6, Report for 1910. 

Complete computations have been made for 124 gravity stations in the United States by 
the three methods of reduction and the results are shown in the two following tables. 

The theoretical value of gravity at sea level was computed by Helmert’s formula 1 of 1901 
for the Potsdam system, namely, 

7-0 = 978.030 (1+0.005302 sin 2 </>- 0.000007 sin 2 2</>). 

The correction for elevation of station was computed by the formula —0.0003086 II, in 
which H is the elevation in meters. It should be carefully noted that this is the reduction 
from sea level to the station, a correction to the theoretical value not to the observed value. 
This correction takes account of the increased distance of the station from the attracting mass, 
as if the station were in the air and there were no irregularities in the earth’s surface (or 
topography). 

The correction for topography and compensation for the new-method reduction was 
computed with the reduction tables shown on pages 30-47 of Special Publication No. 10, and 
the resultant effect was applied as a correction to the theoretical value at sea level. 

These corrections are usually applied to the observed values and the results are compared 
with the theoretical value of gravity at sea level. The method employed in this publication 
and in Special Publication No. 10 appears to be the more logical one. 

The computed value of gravity at the station g c is the theoretical value of gravity at sea 
level, y 0 , corrected for elevation and for topography and compensation. It is therefore directly 
comparable with g, the observed value of gravity at the station. The column g~g c therefore 
represents the departures of the observed values from computed values based upon the 
Helmert formula of 1901 upon the usual reduction for elevation, and upon the new-method 
reductions that take account of topography and compensation. 

All observed values, g, in the following table depend upon relative determinations with the 
half-second pendulums and are based on 980.112 dynes (in centimeter-gram-second units) as 
the absolute value of gravity at the Coast and Geodetic Survey Office at Washington. This 
value depends upon the absolute determination of the value of gravity at Potsdam, 2 Germany, 
and upon the relative values of gravity at Potsdam and Washington, as determined by Mr. 
G. R. Putnam in 1900. 3 

1 The Helmert formula for the Vienna system was hy mistake used in the computations of gravity at sea level in Coast and Geodetic Survey 
Special Publication No. 10, The Effect of Topography and Isostatic Compensation upon the Intensity of Gravity. The Vienna formula is identical 
with that for Potsdam, except that the first term is 978.046. # The difference between the two, 0.016, made an error of that amount in each of the 
anomalies by the two older methods of reduction. It did not, however, make any material changes necessary in the conclusions drawn from the 
results of the investigation. See footnotes on pp. 12 and 75 of Special Publication No. 10. 

2 Bestimmung der Absoluten Grosze der Schwerkraft zu Potsdam mit Reversionspendeln von Prof. Dr. F. Kiihnen und, Prof. Dr. Ph. Furt- 
wangler, Seite 380. 

3 Determination of Relative Value of Gravity in Europe and the United States in 1900, G. R. Putnam, Appendix 5, Coast and Geodetic Survey 

Report, 1901, pp. 354-355. » 



EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY 


9 


The value for Washington was changed from 980.111, the value used in Special Publication 
No. 10, to 980.112 by a new adjustment of the net of gravity stations. (See pp. 25 and 244 
of third volume, by Dr. E. Borrass in 1911, of the Report of the Sixteenth General Conference 
of the International Geodetic Association at London and Cambridge in 1909.) 


Table of principal fads for 124 gravity stations in the United States. 


Number and name of station 

4> 

A 


H 

r* 

Correc¬ 
tion for 
eleva¬ 
tion 

Correc¬ 
tion for 
topogra¬ 
phy and 
compen¬ 
sation 

Com¬ 
puted 
gravity 
at sta¬ 
tion (0 C ) 

Observed 
gravity 
at sta¬ 
tion (g) 

(ff-ffc) 

1. Key West, Fla. 

o 

24 

/ 

33.6 

o 

81 

/ 

48.4 

Meter?. 

1 

978.922 

0.000 

+0.032 

978.954 

978.970 

+0.016 

2. West Palm Beach, Fla. 

26 

42.8 

80 

02.8 

2 

979.073 

- .001 

+ .031 

979.103 

979.129 

+ .026 

3. Punta Gorda, Fla. 

26 

56.2 

82 

03 

1 

979.089 

.000 

+ .020 

979.109 

979.127 

+ .018 

4. Apalachicola, Fla. 

29 

43.5 

84 

58.8 

4 

979.300 

- .001 

+ .015 

979.314 

979.322 

+ .008 

5. New Orleans, La. 

29 

57.0 

90 

04.2 

2 

979.317 

- .001 

+ .013 

979.329 

979.324 

- .005 

6. Rayville, La. 

32 

28 

91 

45 

26 

979.519 

- .008 

+ .008 

979.519 

979.543 

+ .024 

7. Galveston, Tex. 

29 

18.2 

94 

47.5 

3 

979.267 

- .001 

+ .007 

979.273 

979.272 

- .001 

8. Point Isabel, Tex. 

26 

04.7 

97 

12.4 

8 

979.028 

- .002 

+ .015 

979.041 

979.076 

+ .035 

9. Laredo, Tex. 

27 

30.5 

99 

31.2 

129 

979.131 

- .040 

+ .003 

979.094 

979.082 

- .012 

10. Austin, Tex. (capital) 

11. Austin, Tex. (university) 

30 

16.5 

97 

44.3 

170 

979.343 

- .052 

- .003 

979.288 

979.288 

.000 

30 

17.2 

97 

44.2 

189 

979.344 

- .058 

- .001 

979.285 

979.283 

- .002 

12. McAlester, Okla. 

34 

56.2 

95 

46.2 

240 

979. 725 

- .074 

+ .001 

979.652 

979.633 

- .019 

13. Little Rock, Ark. 

34 

45.0 

92 

16.4 

89 

979.709 

- .027 

+ .001 

979.683 

979.721 

+ .038 

14. Columbia, Term. 

35 

36.7 

87 

02.5 

207 

979.783 

- .064 

+ .006 

979. 725 

979. 759 

+ .034 

15. Atlanta, Ga. 

33 

45.0 

84 

23.3 

324 

979.625 

- .100 

+ .014 

979.539 

979.524 

- .015 

16. McCormick, S. C. 

33 

54.8 

82 

18.0 

163 

979.639 

- .050 

+ .012 

979.601 

979.624 

+ .023 

17. Charleston, S. C. 

32 

47.2 

79 

56.0 

6 

979.545 

- .002 

+ .016 

979.559 

979.546 

- .013 

18. Beaufort, N. C. 

34 

43.1 

76 

39.8 

1 

979.706 

.000 

+ .036 

979.742 

979.729 

- .013 

19. Charlottesville, Va. 

38 

02.0 

78 

30.3 

166 

979.992 

- .051 

+ .002 

979.943 

979.938 

- .005 

20. Deer Park, Md. 

39 

25.0 

79 

19.8 

770 

980.114 

- .238 

+ .041 

979.917 

979.935 

+ .018 

21. Washington, D. C. (Coast and Geodetic 
Survey Office) 

38 

53.2 

77 

00.5 

14 

980.067 

- .004 

+ .004 

980.067 

980.112 

+ .045 

22. Washington, D. C. (Smithsonian Insti¬ 
tution) 

38 

53.3 

77 

01.5 

10 

980.067 

- .003 

+ .003 

980.067 

980.114 

+ .047 

23. Baltimore, Md. 

39 

17.8 

76 

37.3 

30 

980.103 

- .009 

+ .006 

980.100 

980.097 

- .003 

24. Philadelphia, Pa. 

39 

57.1 

75 

11.7 

16 

980.162 

- .005 

+ .009 

980.166 

980.196 

+ .030 

25. Princeton, N. J. 

40 

21.0 

74 

39.5 

64 

980.196 

- .020 

+ .013 

980.189 

980.178 

- .011 

26. Hoboken, N. J. 

40 

44 

74 

02 

11 

980.232 

- .003 

+ .008 

980.237 

980.269 

+ .032 

27. New York, N. Y. 

40 

48.5 

73 

57.7 

38 

980.238 

- .012 

+ .011 

980.237 

980.267 

+ .030 

28. Worcester, Mass. 

42 

16.5 

71 

48.5 

170 

980.370 

- .052 

+ .018 

9S0.336 

980.324 

- .012 

29. Boston, Mass. 

42 

21.6 

71 

03.8 

22 

980.377 

- .007 

+ .013 

980.383 

980.396 

+ .013 

30. Cambridge, Mass. 

42 

22.8 

71 

07.8 

14 

980.379 

- .004 

+ .010 

980.385 

980.398 

+ .013 

31. Calais, Me. 

45 

11.2 

67 

16.9 

38 

980.633 

- .012 

+ .010 

980.631 

980.631 

.000 

32. Ithaca, N. Y. 

42 

27.1 

76 

29.0 

247 

980.386 

- .076 

+ .005 

980.315 

980.300 

- .015 

33. Cleveland, Ohio 

34. Cincinnati, Ohio 

41 

30.4 

81 

36.6 

210 

980.301 

- .065 

.000 

980.236 

980.241 

+ .005 

39 

08.3 

84 

25.3 

245 

980.089 

- .076 

+ .002 

980.015 

980.004 

- .011 

35. Terre Haute, Ind. 

39 

28.7 

87 

23.8 

151 

980.119 

- .047 

+ .001 

980.073 

980.072 

- .001 

36. Chicago, Ill. 

41 

47.4 

87 

36.1 

182 

980.326 

- .056 

+ .007 

980.277 

980.278 

+ .001 

37. Madison, Wis. 

43 

04.6 

89 

24.0 

270 

980.442 

- .083 

+ .003 

980.362 

980.365 

+ .003 

38. St. Louis, Mo. 

38 

38.0 

90 

12.2 

154 

980.045 

- .048 

+ .001 

979.998 

980.001 

+ .003 

39. Kansas City, Mo. 

39 

05.8 

94 

35.4 

278 

980.0S5 

- .086 

- .001 

979.998 

979.990 

- .008’ 

40. Ellsworth, Kans. 

38 

43.7 

98 

13.5 

469 

980.053 

- .145 

- .004 

979.904 

979.926 

+ .022 

41. Wallace, Kans. 

38 

54.7 

101 

35.4 

1,005 

980.069 

- .310 

.000 

979. 759 

979.755 

- .004 

42. Colorado Springs, Colo. 

38 

50.7 

104 

49.0 

1,841 

980.064 

- .568 

- .007 

979.489 

979.490 

+ .001 

43. Pikes Peak, Colo. 

38 

50.3 

105 

02.0 

4,293 

980.063 

-1.325 

+ .187 

978.925 

978.954 

+ .029 

44. Denver, Colo. 

39 

40.6 

104 

56.9 

1,638 

980.137 

- .505 

- .015 

979.617 

979.609 

- .008 

45. Gunnison, Colo. 

38 

32.6 

106 

56.0 

2,340 

980.037 

- .722 

- .001 

979.314 

979.342 

+ .028 

46. Grand Junction, Colo. 

39 

04.2 

108 

33.9 

1,398 

980.083 

- .431 

- .051 

979.601 

979.633 

+ .032 

47. Green River, Utah 

38 

59.4 

110 

09.9 

1,243 

980.076 

- . 3S4 

- .043 

979.649 

979.636 

- .013 

48. Pleasant Valley Junction, Utah 

39 

50.8 

111 

00.8 

2,191 

980.152 

- .676 

+ .024 

979.500 

979.512 

+ .012 

49. Salt Lake City, Utah 

40 

46.1 

111 

53.8 

1,322 

980.234 

- .408 

- .041 

979.785 

979.803 

+ .018 

50. Grand Canyon, Wyo. 

51. Norris Geyser Basin, Wyo. 

44 

43.3 

110 

29.7 

2,386 

980.591 

- .736 

+ .038 

979.893 

979.899 

+ .006 

44 

44.2 

no 

42.0 

2,276 

980.592 

- .702 

+ .031 

979.921 

979.950 

+ .029 

52. Lower Geyser Basin, Wyo. 

44 

33.4 

no 

48.1 

2,200 

980.576 

- .679 

+ .028 

979.925 

979.932 

+ .007 

53. Seattle, Wash, (university) 

47 

39.6 

122 

18.3 

58 

980.856 

- .018 

— .020 

980.818 

980.733 

- .085 

54. San Francisco, Cal. 

37 

47.5 

122 

25.7 

114 

979.970 

- .035 

+ .045 

979.980 

979.965 

- .015 

55. Mount Hamilton, Cal. 

37 

20.4 

121 

38.6 

1,2S2 

979.931 

- .396 

+ .120 

979.655 

979.660 

+ .005 

56. Seattle, Wash, (high school) 

47 

36.5 

122 

19.8 

74 

980.851 

- .023 

- .018 

980.810 

980. 725 

- .085 

57. Iron River, Mich. 

46 

05.4 

88 

38.4 

458 

980.714 

- .141 

+ .014 

980.587 

980.633 

+ .046 

58. Ely, Mum. 

47 

48.6 

92 

01.0 

448 

980.870 

- .138 

+ .008 

980.740 

980.771 

+ .031 

59. Pembina, N. Dak. 

48 

58.1 

97 

14.9 

243 

980.974 

— .075 

- .009 

980.890 

980.917 

+ .027 

60. Mitchell, S. Dak. 

43 

41.8 

98 

01.8 

408 

980.498 

- .126 

- .006 

980.366 

980.375 

+ .009 

61. Sweetwater, Tex. 

32 

28.4 

100 

24.1 

655 

979.519 

- .202 

+ .009 

979.326 

979.305 

- .021 

62. Kerrville, Tex. 

30 

01.3 

99 

07.6 

498 

979.323 

- .154 

+ .013 

979.182 

979.221 

+ .039 

63. El Paso, Tex. 

31 

46.3 

106 

29.0 

1,146 

979.462 

- .354 

+ .001 

979.109 

979.124 

+ .015 

64. Nogales, Ariz. 

31 

21.3 

no 

56.6 

1,181 

979. 429 

- .364 

+ .038 

979.103 

979.061 

- .042 

65. Yuma, Ariz. 

32 

43.3 

114 

37.0 

54 

979.539 

- .017 

- .010 

979.512 

979.529 

+ .017 

66. Compton, Cal. 

33 

53.4 

118 

13.2 

20 

979.636 

- .006 

.000 

979.630 

979.588 

- .042 

67. Goldfield, Nev. 

37 

42.2 

117 

14.5 

1,716 

979.963 

- .529 

+ .027 

979.461 

979.456 

- .005 

68. Yavapai, Ariz. 

36 

03.9 

112 

07.1 

2,179 

979.821 

- .672 

+ .034 

979.183 

979.192 

+ .009 

69. Grand Canyon, Ariz. 

36 

05.3 

112 

06.8 

849 

979.823 

- .262 

- .096 

979.465 

979.463 

- .002 

70. Gallup, N. Mex. 

35 

31.8 

108 

44.2 

1,990 

979.775 

- .614 

+ .014 

979.175 

979.170 

- .005 

71. Las Vegas, N. Mex. 

35 

35.8 

105 

12.1 

1,960 

979.781 

- .605 

+ .017 

979.193 

979.204 

+ .011 

72. Shamrock, Tex. 

35 

12.8 

100 

11.4 

708 

979.748 

- .218 

+ .007 

979.537 

979.577 

+ .040 

73. Denison, Tex. 

33 

45.3 

96 

32.8 

230 

979.625 

- .071 

- .001 

979.553 

979.566 

+ .013 

74. Minneapolis, Minn. 

44 

58.7 

93 

13.9 

256 

980.614 

- .079 

- .005 

980.530 

980.597 

+ .067 

75. Lead, S. Dak. 

44 

21.1 

103 

45.6 

1,590 

980.557 

- .491 

+ .044 

980. no 

980.170 

+ .060 

76. Bismarck, N. Dak. 

46 

48.5 

100 

47.0 

516 

980.779 

- .159 

- .005 

980.615 

980.625 

+ .010 

77. Hinsdale, Mont. 

48 

23.8 

107 

05.3 

661 

980.923 

- .204 

- .017 

980.702 

980.739 

+ .037 

78. Sandpoint, Idaho. 

48 

16.4 

116 

33.3 

637 

980.911 

- .197 

- .044 

980.670 

980.680 

+ .010 

79. Boise", Idaho 

43 

37.2 

116 

12.3 

821 

980.491 

- .253 

- .042 

980.196 

980.212 

+ .016 
















10 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


Table of principal fads for 12 ^ gravity stations in the United States —Continued. 









Correc- 

Correc¬ 
tion for 

Com¬ 
puted 
gravity 
at sta¬ 
tion (ff 0 ) 

Observed 


Number and name of station 

<t> 

1 


H 

To 

tion for 
eleva- 

topogra¬ 
phy and 

gravity 
at sta- 

(ff-ffc) 








tion 

compen¬ 

sation 

tion ( g ) 



° 

, 

0 

, 

Meters. 







80. Astoria, Oreg. 

46 

11.3 

123 

50.2 

1 

980.724 

0.000 

+0.008 

980.732 

980.727 

-0.005 

81. Sisson, Cal. 

41 

18.3 

122 

19.6 

1,048 

980.282 

- .323 

+ .015 

979.974 

979.972 

- .002 

82. Rock Springs, Wyo. 

41 

35.1 

109 

13.2 

1,910 

980.308 

- .589 

- .001 

979.718 

979. 739 

+ .021 

83. Paxton, Nebr. 

84. Washington, D. C. (Bureau of Standards) 

41 

07.4 

101 

21.3 

932 

980.266 

- . 2S8 

+ .002 

979.980 

979.982 

+ .002 

38 

56.3 

77 

04.0 

103 

980.070 

- .032 

+ .012 

980.050 

980.095 

+ .045 

85. North Hero, Vt. 

86. Lake Placid, N. Y. 

44 

49.1 

73 

17.5 

35 

980.599 

- .011 

- .009 

980.579 

980.588 

+ .009 

44 

17.5 

73 

59.1 

571 

980.551 

- .176 

+ .032 

980.407 

980. 421 

+ .014 

87. Potsdam, N. Y. 

44 

40.1 

74 

58.8 

130 

980.586 

- .040 

- .004 

980.542 

980.571 

+ .029 

88. Wilson, N. Y. 

43 

18.4 

78 

49.6 

87 

980.462 

- .027 

- .002 

980.433 

980.431 

- .002 

89. Alpena, Mich. 

45 

03.8 

83 

27.0 

178 

980. 622 

- .055 

.000 

980.567 

980.555 

- .012 

90. Virginia Beach, Va. 

36 

50.5 

75 

58.4 

4 

979.888 

- .001 

+ .025 

979.912 

979.872 

- .040 

91. Durham, N. C. 

36 

00.2 

78 

53.5 

126 

979.816 

- .039 

+ .014 

979.791 

979.835 

+ .044 

92. Fernandina, Fla. 

30 

40.2 

81 

27.7 

3 

979.374 

- .001 

+ .017 

979.390 

979. 408 

+ .018 

93. Wilmer, Ala. 

30 

49.2 

88 

20.5 

69 

979.386 

- .021 

+ .018 

979.383 

979. 347 

- .036 

94. Aiiceville, Ala. 

33 

07.6 

88 

10.8 

61 

979. 572 

- .019 

+ .008 

979.561 

979. 552 

- .009 

95. New Madrid, Mo. 

36 

35.5 

89 

31.6 

79 

979. 867 

- .024 

+ .001 

979.844 

979.853 

+ .009 

96. Mena, Ark. 

34 

35.2 

94 

14.6 

368 

979.695 

- .114 

+ .015 

979.596 

979. 552 

- .044 

97. Nacogdoches, Tex. 

31 

36.2 

94 

37.8 

92 

979. 448 

- .029 

+ .008 

979.427 

979.424 

- .003 

98. Alpine, Tex. 

30 

21.5 

103 

39.7 

1,359 

979.349 

- .420 

+ .033 

978.962 

978.991 

+ .029 

99. Farwell, Tex. 

34 

23.2 

103 

01.8 

1,259 

979.678 

- .388 

+ .011 

979.301 

979.293 

- .008 

100. Guymon, Okla. 

36 

40.7 

101 

28.7 

949 

979. 874 

- .293 

- .001 

979.580 

979.571 

- .009 

101. Helenwood, Tenn. 

36 

25.9 

84 

32.6 

422 

979.853 

- .130 

+ .015 

979.738 

979. 786 

+ .048 

102. Cloudland, Tenn. 

36 

06.2 

S2 

07.9 

1,890 

979.824 

- .583 

+ .130 

979.371 

979.383 

+ .012 

103. Hughes, Tenn. 

36 

08.5 

82 

07.2 

994 

979.827 

- .306 

+ .053 

979.574 

979.553 

- .021 

104. Charleston, W.Va. 

38 

20.9 

81 

37.7 

184 

980.019 

- .057 

- .010 

979.952 

979.936 

- .016 

105. State CoLege, Pa. 

106. Fort Kent, Me. 

40 

47.9 

77 

51.8 

358 

980.237 

- .110 

+ .010 

980.137 

980.124 

- .013 

47 

14.9 

68 

36.0 

160 

9S0.818 

- .049 

+ .001 

980.770 

980.765 

- .005 

107. Prentice, Wis. 

108. Fergus Falls, Minn. 

45 

32.6 

90 

17.8 

469 

980.665 

- .145 

+ .010 

980.530 

980.562 

+ .032 

46 

17.2 

96 

05.0 

366 

980.732 

- .113 

+ .001 

9S0.620 

980.622 

+ .002 

109. Sheridan, Wyo. 

44 

48.0 

106 

58. 7 

1,150 

980.598 

- .355 

- .031 

980.212 

980.252 

+ .040 

110. Boulder, Mont. 

46 

14.2 

112 

07.3 

1,493 

980. 727 

- .461 

- .007 

980.259 

980.252 

- .007 

111. Skykomish, Wash. 

47 

42.4 

121 

22.3 

280 

980.860 

- .086 

- .047 

980.727 

980.707 

- .020 

112. Olympia, Wash. 

47 

03.4 

122 

52.7 

19 

980.802 

- .006 

- .012 

980.784 

980.825 

+ .041 

113. Heppner, Oreg. 

114. Truekee, Cal. 

45 

39 

21.4 

19.6 

119 

120 

33.2 

11.4 

598 

1,805 

980.648 
9S0.105 

- .185 

- .557 

- .007 
+ .057 

980.456 
979.605 

980. 437 
979. 585 

- .019 

- .020 

115. Winnemucca, Nev. 

40 

58.4 

117 

43.8 

1,311 

980.253 

- .404 

- .004 

979.845 

979.844 

- .001 

116. Elv, Nev. 

39 

14.9 

114 

53.4 

1,962 

980.099 

- .605 

+ .020 

979.514 

979.501 

- .013 

117. Guernsey, Wyo. 

42 

16. 1 

104 

44.0 

1,322 

980.369 

- . 40S 

- .016 

979.945 

979.989 

+ .044 

118. Pierre, S. Dak. 

44 

21.9 

100 

20.8 

454 

980.558 

- .140 

- .013 

980.405 

980. 427 

+ .022 

119. Fort Dodge, Iowa. 

42 

30.8 

94 

11.4 

340 

980.391 

- .105 

+ .002 

980.288 

980.311 

+ .023 

120. Keithsburg, Ill. 

41 

06.4 

90 

57 

167 

980.265 

- .051 

- .003 

980.211 

980.211 

000 

121. Grand Rapids, Mich. 

42 

58.0 

85 

40.8 

236 

9»0.432 

- .073 

+ .003 

980.362 

9S0. 372 

+ .010 

122. Angola, Ind. 

41 

37.7 

85 

00.6 

318 

980.312 

- .098 

+ .011 

980.225 

980.244 

+ .019 

123. Albany, N. Y. 

42 

39.1 

73 

46.1 

61 

980.404 

- .019 

- .006 

980.379 

980. 344 

- .035 

124. Port Jervis, N. Y. 

41 

22.4 

74 

41.1 

141 

980.288 

- .044 

+ .003 

980.247 

980.222 

- .025 


CORRECTION TO HELMERT’S FORMULA OF 1901. 

The mean of the above values of g — g c is +0.006 dyne and the probable error of a single 
value is ±0.017 dyne. The two residuals from this mean for the two Seattle stations are each 
— 0.091 dyne, which is more than five times the probable error of a single value. It is believed 
that these anomalies are caused by some very unusual local disturbance and consequently 
should be rejected from the list of anomalies before taking means. 

After rejecting the two Seattle stations the probable error of a single value of g — g c is 
±0.016 dyne. The mean value of g — g c with regard to sign is +0.008 ±0.0014 dyne. As this 
mean is five times its own probable error it is believed that it represents a real correction to the 
Helmert formula of 1901 for the theoretical value of gravity at sea level, and that this correc¬ 
tion should be applied in connection with the new method of reduction for topography and 
compensation. Accordingly in the following tables the quantities called “Anomaly, New 
method” are g— (p c + 0.008) in dynes. These are, therefore, the anomalies in gravity as given 
by the new method and referred to the following formula for the theoretical value of gravity at 
sea level: 

ro = 978.038 (1+0.005302 sin 2 cp- 0.000007 sin 2 2 cp'), 

this being Ilelmert’s formula of 1901 (for the Potsdam system) with a constant correction 
of +0.008 to the first term. This is equivalent to changing Helmert’s derived value of gravity 
at the equator but with his flattening retained. The reciprocal of the flattening as derived 
from gravity observations in the United States is given on page 25. 





















EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


11 


A plus sign of the anomaly means that at the station in question the intensity of gravity 
is in excess of that which would occur there if the isostatic compensation were complete and 
uniformly distributed to the depth of 113.7 kilometers, while if the anomaly is minus the intensity 
of gravity is less than it would be if the compensation were complete and uniformly distributed 
to the depth of 113.7 kilo; leters. 


COMPARISON OF APPARENT ANOMALIES BY THE NEW AND OLD METHODS. 

The values g 0 " — jo and of g 0 — y 0 in the following tables have the same meaning as in the 
reports of the International Geodetic Association. 

The quantity g 0 " — Jo is the apparent anomaly when the Helmert formula of 1901 and the 
Bouguer reduction are used. The Bouguer reduction “has been very generally applied m 

reducing pendulum observations to the level of the sea. This formula is dg = + ~ r ~( 1 — ^ V 

where dg is the correction to observed gravity, g is gravity at sea level, II is elevation above 
sea level, r is radius of the earth, d is density of matter lying above sea level, and A is mean 
density of the earth. The first term takes account of the distance from the earth’s center, 
and the second term of the vertical attraction of the matter lying between the sea level and 
station, on the supposition that the latter is located on an indefinitely extended horizontal 
plain. Wherever the topography about a station departs materially from this condition of a 
horizontal plain a third term must be added to the above formula, being a correction to the 
second term or to observed gravity on account of such irregularities.” 1 The Bouguer reduc¬ 
tion thus takes no account of isostatic compensation and neglects all curvature of the sea-level 
surface, the topography being treated as if it were standing on a plane of indefinite extent. 

The quantity g 0 — jo is the apparent anomaly when the Helmert formula of 1901 is used in 
connection with the so-called reduction to sea level in free air only (0.0003086 H). This 
reduction ignores both the topography and the isostatic compensation. It takes account 
simply of the increased distance of the station from the earth’s center when the station is above 
sea level. 

A comparison of the anomalies by the new method, on the one hand, with those by the 
two older methods, as shown in the columns headed g 0 " — y 0 , and g 0 — y 0 , on the other hand, will 
therefore show the merits of the new method of reduction in comparison with the Bouguer 
and the free-air methods. 

The comparison of the new method is made with the Bouguer and free-air reductions, 
for the Bouguer reduction postulates a total lack of compensation and a consequent high rigidity 
of the earth’s crust while the free-air method assumes that each piece of topography is com¬ 
pletely compensated for at zero depth. Besides, the Bouguer and free-air methods are those 
which are now most generally used. 

1 This excellent statement of the nature of the Bouguer reduction is quoted from Mr. G. R. Putnam. (See Appendix 1 of the Coast and Geo¬ 
detic Survey Report for 1S94, pp. 21-22.) 



12 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY 


Number and name of station 

Anomaly 

Numbei and name of station 

Anomaly 

New method 
g —(f7o+0.008) 

Bouguer 

{go"—To) 

In fiee air 

{go—To) 

New method 

9 —(0C+O.OO8) 

Bouguer 
{go"—To) 

In free air 

{go—To) 

1. Key West, Fla. 

+0.008 

+0.048 

+0.048 

62. Kerrville, Tex. 

+ .031 

- .003 

+ .052 

2. West Palm Beach, Fla. 

+ .018 

+ .057 

+ .057 

63. El Paso, Tex. 

+ .007 

- .111 

+ .016 

3. Punta Gorda, Fla. 

+ .010 

+ .038 

+ .038 

64. Nogales, Ariz. 

- .050 

- .132 

- .004 

4. Apalachicola, Fla. 

000 

+ .023 

+ .023 

65. Yuma, Ariz. 

+ .009 

+ .001 

+ .007 

5. New Orleans, La. 

- .013 

+ .008 

+ .008 

66. Compton, Cal. 

- .050 

- .041 

- .042 

6. Rayville, La. 

+ .016 

+ .029 

+ .032 

67. Goldfield, Nev. 

- .013 

- .166 

+ .022 

7. Galveston, Tex. 

- .009 

+ .006 

+ .006 

68. Yavapai, Ariz. 

+ .001 

- .162 

+ .043 

8. Point Isabel, Tex. 

+ .027 

+ .049 

+ . 050 

69. Grand Canyon, Ariz. 

- .010 

- .173 

- .098 

9. Laredo, Tex. 

- .020 

- .022 

- .009 

70. Gallup, N. Mex. 

- .013 

- .211 

+ .009 

10. Austin, Tex. (capitol) 

- .008 

- .021 

- .003 

71. Las Vegas, N. Mex. 

+ .003 

- .189 

+ .028 

11. Austin, Tex. (university) 

- .010 

- .023 

- .003 

72. Shamrock, Tex. 

+ .032 

- .031 

+ .047 

12. McAlester, Okla. 

- .027 

- .045 

- .018 

73. Denison, Tex. 

+ .005 

- .012 

+ .012 

13. Little Rock, Ark. 

+ .030 

+ .030 

+ .039 

74. Minneapolis, Minn. 

+ .059 

+ .034 

+ .062 

14. Columbia, Tenn. 

+ .026 

+ .017 

+ .040 

75. Lead, S. Dak. 

+ .052 

- .072 

+ .104 

15. Atlanta, Ga. 

- .023 

- .036 

- .001 

76. Bismarck, N. Dak. 

+ .002 

- .052 

+ .005 

16. McCormick, S. C. 

+ .015 

+ .017 

+ .035 

77. Hinsdale, Mont. 

+ .029 

- .053 

+ .020 

17. Charleston, S. C. 

- .021 

+ .003 

+ .003 

78. Sandpoint, Idaho 

+ .002 

- .105 

- .034 

18. Beaufort, N. C. 

- .021 

+ .023 

+ .023 

79. Boise, Idaho 

+ .008 

- .117 

- .026 

19. Charlottesville, Va. 

- .013 

- .021 

- .003 

80. Astoria, Oreg. 

- .013 

+ .003 

+ .003 

20. Deer Park, Md. 

+ .010 

- .019 

+ .059 

81. Sisson, Cal. 

- .010 

- .103 

+ .013 

21. Washington, D. C. (Coast 




82. Rock Springs, Wyo. 

+ .013 

- .191 

+ .020 

and Geodetic Suivey 




83. Paxton, Nebr. 

- .006 

- .099 

+ .004 

Office) 

+ .037 

+ .048 

+ .049 

84. Washington, D. C.(Bureau 




22. Washington, D. C. (Smith- 




of Standards) 

+ .037 

+ .046 

+ .057 

sonian Institution) 

+ .039 

+ .049 

+ .050 

85. North Hero. Vt. 

+ .001 

- .004 

000 

23. Baltimore, Md. 

- .011 

000 

+ .003 

86. Lake Placid, N. Y. 

+ .006 

- .017 

+ .046 

24. Philadelphia. Pa. 

+ .022 

+ .037 

+ .039 

87. Potsdam, N. Y. 

+ .021 

+ .011 

+ .025 

25. Princeton, N. J. 

- .019 

- .004 

+ .002 

88. Wilson, N. Y. 

- .010 

- .014 

- .004 

26. Hoboken, N. I. 

+ .024 

+ .039 

+ .040 

89. Alpena, Mich. 

- .020 

- .032 

- .012 

27. New York, N. Y. 

+ .022 

+ .037 

+ .041 

90. Virginia Beach, Va. 

- .048 

- .015 

- .015 

28. Worcester, Mass. 

- .020 

- .014 

+ .006 

91. Durham^ N. C. 

+ .036 

+ .045 

+ .058 

29. Boston, Mass. 

+ .005 

+ .024 

+ .026 

92. Fernandina, Fla. 

+ .010 

+ .036 

+ .035 

30. Cambridge, Mass. 

+ .005 

+ .022 

+ .023 

93. Wilmer. Ala. 

- .044 

- .027 

- .018 

31. Calais, Me. 

- .008 

+ .006 

+ .010 

94. Aliceville, Ala. 

- .017 

- .010 

- .001 

32. Ithaca, N. Y. 

- .023 

- .033 

- .010 

95. New Madrid, Mo. 

+ .001 

+ .001 

+ .010 

33. Cleveland, Ohio. 

- .003 

- .016 

+ .005 

96. Mena, Ark. 

- .052 

- .066 

- .029 

34. Cincinnati, Ohio. 

- .019 

- .034 

- .009 

97. Nacogdoches, Tex. 

- .011 

- .005 

+ .005 

35. Terre Haute, Ind. 

- .009 

- .016 

000 

98. Alpine, Tex. 

+ .021 

- .088 

+ .062 

36. Chicago, Ill. 

- .007 

- .012 

+ .008 

99. Farwell,Tex. 

- .016 

- .132 

+ .003 

37. Madison, Wis. 

- .005 

- .024 

+ .006 

100. Guymon, Okla. 

- .017 

- .110 

- .010 

38. St. Louis, Mo. 

- .005 

- .014 

+ .004 

101. Helenwood, Tenn. 

+ .040 

+ .015 

+ .063 

39. Kansas City, Mo. 

- .016 

- .038 

- .009 

102. Cloudland, Tenn. 

+ .004 

- .042 

+ .142 

40. Ellsworth, Kans. 

+ .014 

- .029 

+ .016 

103. Hughes, Tenn. 

- .029 

- .074 

+ .032 

41. Wallace, Kans. 

- .012 

- .105 

- .004 

104. Charleston. W. Va. 

- .024 

- .045 

- .026 

42. Colorado Springs, Colo. 

- .007 

- .188 

- .006 

105. State College, Pa. 

- .021 

- .038 

- .003 

43. Pikes Peak, Colo. 

+ .021 

- .204 

+ .216 

106. Fort Kent, Me. 

- .013 

- .021 

- .004 

44. Denver, Colo. 

- .016 

- . 182 

- .023 

107. Prentice, Wis. 

+ .024 

- .005 

+ .042 

45. Gunnison, Colo. 

+ .020 

- .229 

+ .027 

108. Fergus Falls, Minn. 

- .006 

- .034 

+ .003 

46. Grand Junction, Colo. 

+ .024 

- .158 

- .019 

109. Sherdian, Wyo. 

+ .032 

- .116 

+ .009 

47. Green River, Utah. 

- .021 

- . 180 

- .056 

110. Boulder, Mont. 

- .015 

- .181 

- .014 

48. Pleasant Valley Junction, 




111. Skykomish, Wash. 

- .028 

- .087 

- .067 

Utah 

+ .004 

- .187 

+ .036 

112. Olympia, Wash. 

+ .033 

+ .026 

+ .029 

49. Salt Lake City, Utah. 

+ .010 

- . 146 

- .023 

113. Heppner, Oreg. 

- .027 

- .093 

- .026 

50. Grand Canyon, Wyo. 

- .002 

- .208 

+ .044 

114. Truckee,Cal. 

- .028 

- .162 

+ .037 

51. Norris Geyser Basin, Wyo. 

+ .021 

- .177 

+ .060 

115. Winnemucca, Nev. 

.009 

- .150 

— .005 

52. Lower GeVser Basin, Wyo. 

- .001 

- . 193 

+ .035 

116. Ely, Nev. 

- .021 

- .207 

+ .007 

53. Seattle, Wash.(university) 

- .093 

- .111 

- .105 

117. Guernsey, Wyo. 

+ .036 

- .113 

+ .028 

54. San-Francisco, Cal. 

- .023 

+ .019 

+ .004 

118. Pierre, S. Dak. 

+ .014 

- .039 

+ .009 

55. Mount Hamilton, Cal. 

- .003 

+ .003 

+ .125 

119. Fort Dodge, Iowa 

+ .015 

- .011 

+ .025 

56. Seattle, Wash. (high school) 

- .093 

- .111 

- .103 

120. Keithsburg, Ill. 

- .008 

- .018 

- .003 

57. Iron River, Mich. 

+ .038 

+ .009 

+ .060 

121. Grand Rapids, Mich. 

+ .002 

- .008 

+ .013 

58. Ely, Minn. 

+ .023 

- .010 

+ .039 

122. Angola, Ind. 

+ .011 

- .001 

+ .030 

59. Pembina, N. Dak. 

+ .019 

- .008 

+ .018 

123. Albany, N. Y. 

- .043 

- .048 

- .041 

60. Mitchell, S. Dak. 

+ .001 

- .040 

+ .003 

124. Port Jervis, N. Y. 

- .033 

- .035 

- .022 

61. Sweetwater, Tex. 

- .029 

- .084 

- .012 






For all the stations treated as a single group the means are as follows: 



Anomaly 


New 

method 

Bouguer 

In free air 

Mean with regard to sign 124 stations 

-0.002 

-0. 050 

+0.014 

Mean without regard to sign 124 stations 

Mean with regard to sign 122 stations (Seattle stations 

.020 

.064 

.029 

omitted) 

Mean without regard to sign 122 stations (Seattle stations 

.000 

- .048 

+ .016 

omitted) 

.018 

.063 

.028 


The mean without regard to sign for the new-method anomalies is only two-thirds that for 
the free-air anomalies and about three-tenths that for the Bouguer anomalies. At most of the 
stations the new-method anomalies are smaller than the free-air and the Bouguer anomalies. 
































EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


13 


The maximum new-method anomaly is —0.093 at the Seattle stations, Nos. 53 and 56, while the 
maximum free-air anomaly is +0.216 at station 43 (Pikes Peak) and the maximum Bouguer 
anomaly is —0.229 at station 45 (Gunnison). 

An analysis of the above tables indicates clearly that the new method of reduction is much 
closer to the truth than either the Bouguer or the free-air methods of reduction. 

The distribution, according to size, of the anomalies by the three methods of reduction 
is shown in the following table: 


Limits in dynes 

Number of anomalies 

Limits in dynes 

Number of anomalies 

New 

method 

Bouguer 

In free air 

New 

.method 

Bouguer 

In free air 

0.200 to 0.300 

0 

5 

1 

0.050 to 0.060 

5 

3 

8 

0.100 to 0.200 

0 

28 

5 

0.040 to 0.050 

4 

12 

12 

0.090 to 0.100 

2 

2 

1 

0.030 to 0.040 

12 

17 

13 

0.0S0 to 0.090 

0 

3 

0 

0.020 to 0.030 

32 

14 

20 

0.070 to 0.080 

0 

2 

0 

0.010 to 0.020 

34 

19 

17 

0.060 to 0.070 

0 

1 

6 

0.000 to 0.010 

35 

18 

41 


An inspection of the data in this table shows that the anomalies of the new method are 
distributed in fair agreement with the law of distribution of accidental errors. There is no indi¬ 
cation of any decided systematic error for those anomalies. On the other hand, the distribution 
of the anomalies by each of the older methods of reduction departs greatly from the law of dis¬ 
tribution of accidental errors and indicates that there are substantial systematic errors present. 

DISCUSSION OF ERRORS. 

It is important to know the degree of reliability of the values of gravity at the stations used 
in this investigation in order to be able to estimate the extent to which errors from different 
sources may affect the apparent anomahes. The subject of the errors and their effects on the 
anomalies is dealt with exhaustively in Special Publication No. 10, and here only a summary 
of what was stated there will be given. 

The value of the intensity of gravity at a station is subject to uncertainties on account of 
the observations which are represented by a probable error of ±0.0018 dyne on an average. It is 
probable that at no station is the actual error from this source greater than 0.0072 dyne. There 
are also small errors present in each of the operations necessary in the computations of the 
gravity anomalies. The methods adopted in the computing practically eliminate any system¬ 
atic errors and those remaining must be considered as belonging to the accidental class. The 
errors from the several sources are nearly or quite independent of each other and follow different 
laws of distribution. In estimating the effects of all these errors at a station one must therefore 
consider them as accidental errors and that their combined effect is the square root of the sum 
of their squares rather than merely their sum. On this basis it is estimated that the probable 
error of the computed anomaly at a station by the new method is about ±0.003 dyne on an 
average. In other words, the chances are even for and against the proposition, that the actual 
error in the computed anomaly at a station is greater than 0.003 dyne. The new method of 
reduction is not subject to hidden or unsuspected errors which would vitiate the results. 

POSSIBLE RELATIONS OF ANOMALIES TO TOPOGRAPHY. 

In the following five tables the stations are arranged in groups according to the topography 
near the station in order to learn whether there are relations between the anomalies and the 
topography. It is important to test the new-method anomalies in this way to ascertain whether 
they follow in size and sign the relations known to exist between the topography and the anom¬ 
alies by the two older methods of reduction. 















14 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY 


Eighteen coast stations, in the order of their distances from the t OOO-fathom, line. 


Number and name of station 

Distance 

from 

1000- 

fathom 

line 

Anomaly 

Number and name of station 

Distance 

from 

1000- 

fathom 

line 

Anomaly 

New 

method 

9~{9c 

+0.008) 

Bouguer 
W-ro ) 

In free 
air 

(do—ro) 

New 
method 
9-{9 c 
+0.008) 

Bouguer 

W-ro) 

In free 
air 

(. 9o~ro) 


Kilo- 





Kilo- 





meters 





meters 




54. San Francisco, Cal. 

85 

-0.023 

+0.019 

+0.004 

2. West Palm Beach, Fla. 

243 

+0.018 

+0.057 

+0.057 

18. Beaufort, N. C. 

95 

- .021 

+ .023 

+ .023 

3. Punta Gorda, Fla. 

280 

+ .010 

+ .038 

+ .038 

80. Astoria, Oreg. 

120 

- .013 

+ .003 

+ .003 

29. Boston ; Mass. 

300 

+ .005 

+ .024 

+ .026 

90. Virginia Beach, Va. 

130 

- .048 

- .015 

- .015 

30. Cambridge, Mass. 

300 

+ .005 

+ .022 

+ .023 

92. Femandina, Fla. 

145 

+ .010 

+ .036 

+ .035 

17. Charleston, S. C. 

305 

- .021 

+ .003 

+ .003 

1. Key W est, Fla. 

150 

+ .008 

+ .048 

+ .048 

7. Galveston, Tex. 

330 

- .009 

+ .006 

+ .006 

8. Point Isabel, Tex. 

160 

+ .027 

+ .049 

+ .050 






5. New Orleans, La. 

210 

- .013 

+ .008 

+ .008 

Mean with regard to 





4. Apalachicola, Fla. 

225 

.000 

+ .023 

+ .023 

sign 


- .004 

+ .021 

+ .021 

27. New York, N. Y. 

225 

+ .022 

+ .037 

+ .041 

Mean without regard to 





26. Hoboken, N. J. 

230 

+ .024 

+ .039 

+ .040 

sign 


.018 

.027 

.027 

66. Compton, Cal. 

230 

— .050 

- .041 

- .042 







Twenty-five stations near the coast, in the order of their distances from the open coast. 


Number and name of station 

Distance 
from the 
open 
coast 

Anomaly 

Number and name of station 

Distance 
from the 
open 
coast 

Anomaly 

New 

method 

9 {.9 c 
+0.008) 

Bouguer 

W-ro) 

In free 
air 

{ 9o~ro) 

New 
method 
9~{9c 
+0.008) 

Bouguer 
{9 o"—r o) 

In free 
air 

{go—ro) 


Kilo- 





Kilo- 





meters 





meters 




31. Calais, Me. 

50 

-0.008 

+0.006 

+0.010 

65. Yuma, Ariz. 

220 

+0.009 

+0.001 

+0.007 

25. Princeton, N. J. 

60 

- .019 

- .004 

+. .002 

97. Nacogdoches, Tex. 

220 

- .011 

- .005 

+ .005 

93. Wilmer, Ala. 

65 

- .044 

- .027 

- .018 

123. Albany, N. Y. 

220 

- .043 

— .048 

- .041 

23. Baltimore, Md. 

75 

- .011 

.000 

+ .003 

16. McCormick, S. C. 

235 

+ .015 

+ .017 

+ .035 

28. Worcester, Mass. 

85 

- .020 

- .014 

+ .006 

10. Austin, Tex. (capitol) 

245 

- .008 

- .021 

- .003 

24. Philadelphia, Pa. 

90 

+ .022 

+ .037 

+ .039 

11. Austin, Tex. (univer- 





124. Port Jervis, N. Y. 

100 

- .033 

- .035 

- .022 

sity) 

245 

- .010 

- .023 

- .003 

81. Sisson. Cal. 

142 

- .010 

- .103 

+ .013 

19. Charlottesville, Va. 

250 

- .013 

- .021 

- .003 

21. Washington, D. C. 





32. Ithaca, N. Y. 

305 

- .023 

- .033 

- .010 

(Coast and Geodetic 





94. Aliceville, Ala. 

305 

- .017 

- .010 

- .001 

Survey Office) 

170 

+ .037 

+ .048 

+ .049 

62. Ejerrville, Tex. 

310 

+ .031 

- .003 

+ .052 

22. Washington, D. C. 





106. Fort Kent, Me. 

315 

- .013 

.021 

- .004 

(Smithsonian Insti- 





6. Rayville, La. 

325 

+ .016 

+ .029 

+ .032 

tution) 

170 

+ .039 

+ .049 

+ .050 






84. Washington, D. C. 





Mean with regard to 





(Bureau of Stand- 





sign 


— .002 

- .004 

+ .012 

ards) 

175 

+ .037 

+ .046 

+ .057 

Mean without regard to 





91. Durham, N. C. 

210 

+ .036 

+ .045 

+ .058 

sign 


.022 

.027 

.021 

9. Laredo, Tex. 

215 

- .020 

- .022 

- .009 







Thirty-nine stations in the interior and not in mountainous regions, arranged in the order of elevation. 


. 



Anomaly 





Anomaly 


Number and. name of station 

Eleva- 

vation 

New 
method 
9~{9c 
+0.008) 

Bouguer 

W-ro) 

In free 
air 

{go—ro) 

N umber and name of station 

Eleva- 

vation 

New 

method 

9-{9c 

+0.008) 

Bouguer 
{9o"-ro) 

In free 
air 

{ 90 —ro) 

95. New Madrid, Mo. 

88. Wilson, N. Y. 

13. Little Rock, Ark. 

Meters 

79 

+0.001 

+0.001 

+0.010 

119. Fort Dodge, Iowa 

Meters 

340 

+0.015 

-0.011 

+0.025 

87 

- .010 

— .014 

- .004 

108. Fergus Falls, Minn. 

366 

- .006 

- .034 

+ .003 

89 

+ .030 

+ .030 

+ .039 

96. Mena, Ark. 

368 

- .052 

- .066 

- .029 

87. Potsdam, N. Y. 

130 

+ .021 

+ .011 

+ .025 

60. Mitchell, S. Dak. 

408 

+ .001 

- .040 

+ .003 

35. Terre Haute, Ind. 

151 

- .009 

- .016 

.000 

58. Ely, Minn. 

448 

+ .023 

- .010 

+ .039 

38. St. Louis, Mo. 

154 

- .005 

- .014 

+ .004 

118. Pierre, S. Dak. 

454 

+ .014 

- .039 

+ .009 

120. Keithsburg, Ill. 

167 

- .008 

- .018 

- .003 

57. Iron River, Mich. 

458 

+ .038 

+ .009 

+ .060 

S9. Alpena, Mich. 

178 

- .020 

- .032 

- .012 

40. Ellsworth, Kans. 

469 

+ .014 

- .029 

+ .016 

36. Chicago, Ill. 

182 

- .007 

- .012 

+ .008 

107. Prentice, Wis. 

469 

+ .024 

- .005 

+ .042 

104. Charleston, W. Va. 

184 

- .024 

- .045 

- .026 

76. Bismarck, N. Dak. 

516 

+ .002 

- .052 

+ .005 

14. Columbia, Tenn. 

207 

+ .026 

+ .017 

+ .040 

61. Sweetwater, Tex. 

655 

- .029 

- .084 

- .012 

33. Cleveland, Ohio 

210 

- .003 

- .016 

+ .005 

77. Hinsdale, Mont. 

72. Shamrock, Tex. 

661 

+ .029 

- .053 

+ .020 

73. Denison, Tex. 

230 

+ .005 

- .012 

+ .012 

708 

+ .032 

- .031 

+ .047 

121. Grand Rapids, Mich. 

236 

+ .002 

- .008 

+ .013 

S3. Paxton, Nebr. 

932 

- .006 

- .099 

+ .004 

12. McAlester, Okla. 

240 

- .027 

- .045 

- .018 

100. Guymon, Okla. 

949 

- .017 

- .110 

- .010 

59. Pembina, N. Dak. 

243 

+ .019 

- .008 

+ .018 

41. Wallace, Kans. 

1005 

- .012 

- .105 

- .004 

34. Cincinnati, Ohio 

74. Minneapolis, Minn. 

37. Madison, Wis. 

39. Kansas City, Mo. 

245 

- .019 

- .034 

- .009 

99. Farwell, Tex. 

1259 

— .016 

— .132 

+ .003 

256 

270 

278 

+ .059 

- .005 

- .016 

+ .034 

- .024 

- .038 

+ .062 
+ .006 
- .009 

Mean with regard to 
sign 


+ .001 

- .030 

+ .011 

122. Angola, Ind. 

15. Atlanta, Ga. 

318 

324 

+ .011 
- .023 

- .001 
- .036 

+ .030 
- .001 

Mean without regard to 
sign 


.017 

.035 

0.18 




























































EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY 


15 


Twenty-two stations in mountainous regions and below the general level arranged in the order of 

their distances below the general level. 


Number and name of 
station 

Average 
elevation 
within 
100 miles 
of station 
minus 
elevation 
of station 

Eleva¬ 
tion of 
station 

Anomaly 

Number and name of 
station 

Average 
elevation 
within 
100 miles 
of station 
minus 
elevation 
of station 

Eleva¬ 
tion of 
station 

Anomaly 

New 

meth¬ 

od 

0-K+ 

0.008) 

Bou- 

guer 

(9o" r 

To) 

In free 
air 

too To) 

New 

meth¬ 

od 

{7“({7c+ 

0.008) 

Bou- 

guer 

Oo"- 

To ) 

In free 
air 

(Qo—To) 


Meters 

Meters 





Meters 

Meters 




70. Gallup, N. Mex. 

30 

1990 

-0.013 

-0.211 

+0.009 

49. Salt Lake City, 






105. State College, Pa. 

33 

358 

- .021 

- .038 

- .003 

Utah 

570 

1322 

+0.010 

-0.146 

-0.023 

67. Goldfield, Nev. 

112 

1716 

- .013 

- . 166 

+ .022 

44. Denver, Colo. 

574 

1638 

- .016 

- .182 

- .023 

85. North Hero, Vt. 

167 

35 

4- .001 

- .004 

000 

79. Boise, Idaho 

575 

821 

4 .008 

- .117 

- .026 

63. El Paso, Tex. 

205 

1146 

4- .007 

- .111 

4 .016 

78. Sandpoint, Idaho 

588 

637 

+ .002 

- .105 

- .034 

113. Heppner, Oreg. 

264 

598 

- .027 

- .093 

- .026 

69. Grand Canyon, 






112. Olympia, Wash. 

306 

19 

+ .033 

+ .026 

4 .029 

Ariz. 

824 

849 

- .010 

- .173 

- .098 

110. Boulder, Mont. 

307 

1493 

- .015 

- .181 

- .014 

46. Grand Junction, 






111. Skykomish, Wash. 

322 

280 

- .028 

- . 087 

- .067 

Colo. 

850 

1398 

+ .024 

- .158 

- .019 

117. Guernsey, Wyo. 

324 

1322 

+ .036 

- .113 

+ .028 

47. Green River, Utah 

870 

1243 

- .021 

- .180 

- .056 

115. Winnemucca, Nev. 

346 

1311 

- .009 

- .150 

- .005 







109. Sheridan, Wyo. 

378 

1150 

+ .032 

- .116 

+ .009 

Mean with regard to 






82. Rock Springs, Wyo. 

379 

1910 

+ .013 

- .191 

4- .020 

sign 



.000 

- .132 

- .011 

45. Gunnison, Colo. 

380 

2340 

+ .020 

- .229 

+ .027 

Mean without re- 






42. Colorado Springs, 






gard to sign 



.017 

.135 

.025 

Colo. 

420 

1841 

- .007 

- .188 

- .006 








Eighteen stations in mountainous regions and above the general level arranged in the order of their 

distances above the general level. 


Number and name of 
station 

Elevation 
of station 
minus 
average 
elevation 
within 
100 miles 

Eleva¬ 
tion of 
station 

Anomaly 

Number and name of 
station 

Elevation 
of station 
minus 
average 
elevation 
within 
100 miles 

Eleva¬ 
tion of 
station 

Anomaly 

New 

meth¬ 

od 

9-(9o+ 

0.008) 

Bou- 

guer 

too''- 

To) 

In free 
air 

too To) 

New 

meth¬ 

od 

<7—(<7o4- 
0.008) 

Bou- 
guer 
(go 

To) 

In free 
air 

too—To) 


Meters 

Meters 





Meters 

Meters 




71. Las Vegas, N. Mex. 

18 

1960 

+0.003 

-0.189 

+0.028 

86. Lake Placid, N. Y. 

306 

571 

40.006 

-0.017 

4-0.046 

116. Ely, Nev. 

19 

1962 

- .021 

- .207 

4- .007 

103. Hughes, Tenn. 

427 

994 

- .029 

- .074 

+ .032 

101. Helen wood, Tenn. 

33 

422 

+ .040 

+ .015 

+ .063 

75. Lead, S. Dak. 

468 

1590 

+ .052 

- .072 

4- .104 

52. Lower Geyser Ba- 






68. Yavapai, Ariz. 

512 

2179 

4- .001 

- .162 

4- .043 

sin, Wyo. 

63 

2200 

- .001 

- .193 

+ .035 

114. Truckee, Cal. 

512 

1805 

- .028 

- .162 

+ .037 

51. Norris Geyser Ba- 






55. Mount Hamilton, 






sin, Wyo. 

139 

2276 

4- .021 

- .177 

4 .060 

Cal. 

1202 

1282 

- .003 

4- -003 

4- .125 

48. Pleasant Valley 






102. Cloudland, Tenn. 

1324 

1890 

4- -004 

- .042 

4- .142 

Junction, Utah 

147 

2191 

+ .004 

- .187 

+ .036 

43. Pikes Peak, Colo. 

2035 

4293 

+ .021 

- .204 

+ .216 

50. Grand Canyon, 












Wyo. 

249 

2386 

- .002 

- .208 

+ .044 

Mean with regard to 






98. Alpine, Tex. 

265 

1359 

+ -021 

- .088 

4- .062 

sign 



+ .003 

- .118 

+ .063 

64. Nogales, Ariz. 

288 

1181 

- .050 

- .132 

- .004 

Mean without re- 






20. Deer Park, Md. 

291 

770 

+ .010 

- .019 

+ .059 

gard to sign 



.018 

.120 

.064 


Mean anomalies. 

WITH REGARD TO SIGN. 



Number of 
stations 

New method 

Bouguer 

In free air 

Coast stations 

18 

-0. 004 

+0. 021 

+0. 021 

Stations near the coast 

25 

- .002 

- .004 

+ .012 

Stations in the interior, not in mountainous regions 

39 

+ .001 

- .030 

+ .011 

Stations in mountainous regions, below the general level 

22 

.000 

- .132 

- .011 

Stations in mountainous regions, above the general level 

18 

+ .003 

- .118 

+ .063 

All stations (except the two Seattle stations) 

122 

.000 

- .048 

+ .016 


WITHOUT REGARD TO SIGN. 


Coast stations 

18 

0. 018 

0. 027 

0. 027 

Stations near the coast 

25 

.022 

.027 

.021 

Stations in the interior, not in mountainous regions 

39 

.017 

.035 

.018 

Stations in mountainous regions, below the general level 

22 

.017 

.135 

.025 

Stations in mountainous regions, above the general level 

18 

.018 

.120 

.064 

All stations (except the two Seattle stations) 

122 

.018 

.063 

.028 


51853°—12-2 






























































16 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


In the table on page — it is shown that the mean new-method anomaly with regard to sign 
is 0.000 and without regard to sign is 0.018. The Seattle stations are omitted in the comparison 
of the anomalies of the several methods of reduction. In no particular would the conclusions 
arrived at be changed if they were retained. 

In the above groups the means of the new-method anomalies with regard to sign are, 
respectively, —0.004, —0.002, +0.001, 0.000, and +0.003; and without regard to sign are 
0.018, 0.022, 0.017, 0.017, and 0.018, respectively. In no case are the means much different 
from the means of the whole group of stations in the United States, and consequently it must 
be concluded that the effect of the topography and its compensation are adequately taken into 
account by the new method, and that the anomalies are due to local cause or causes which have 
no relation to the topography. 

In considering the small anomalies it should be clearly borne in mind that the errors of 
observation and computation may frequently exceed 0.004 dyne, and in rare cases they may be 
as great as 0.010 dyne. (Page 87, Effect of Topography and Isostatic Compensation upon the 
Intensity of Gravity, Special Publication No. 10.) 

The mean Bouguer anomaly with regard to sign for 122 stations (see p. 12) is —0.048 dyne, 
while the means with regard to sign for the anomalies in the above five groups are, respectively, 
+ 0.021, —0.004, —0.030, —0.132, and—0.118. There is a great range in these values, and it 
is seen that the stations in mountainous regions have large negative values, while the mean for 
the coast stations is positive, but nearly zero. The mean Bouguer anomaly without regard to 
sign for all the stations is 0.063, while the mean Bouguer anomaly for the five groups is, 
respectively, 0.027, 0.027, 0.035, 0.135, and 0.120. The mean of the anomalies for the two 
groups of stations in mountainous regions is about twice the size of the mean of all. The 
anomalies at the stations in the other three groups are much smaller, on an average, and are 
more nearly comparable in size to the new-method anomalies. It is clear that the usual relations 
between the Bouguer anomalies and the topography exist in the United States. 

The mean with regard to sign of the free-air anomalies for all of the stations is +0.016. 
(See p. 12.) The mean with regard to sign of the free-air anomalies at coast stations is +0.021, 
which is characteristic of this method of reduction. The mean with regard to sign of the 
anomalies at the stations near the open coast is +0.012, and the mean for the stations in the 
interior, but not in mountainous regions, is +0.011. It will be noticed that these three groups 
tend to have positive anomalies. This is what may be expected, for topography and compen¬ 
sation are neglected, and the resultant effect of the two is positive in most cases. (See table 
on p. 15.) Where the stations are in mountainous regions below the general level, the anomalies 
tend to be negative, which is the sign which might be expected, as the masses above the station 
have the effect of decreasing the force of gravity. The mean with regard to sign for this group 
is — 0.011 dyne. The mean free-air anomaly at the stations in the mountainous regions above 
the general level is +0.063 dyne, which is three times as great as the mean for any other group. 
A little reflection will make it clear that this large positive value results from ignoring the 
topography and compensation. 

The means without regard to sign of the free-air anomalies are, respectively, 0.027, 0.021, 
0.018, 0.025, and 0.064. The anomalies at coast stations and in mountainous regions are very 
much larger than the mean new-method anomaly. The stations back from the coast and the 
stations in the interior not in mountainous regions have anomalies which are, on an average, 
about equal to the mean new-method anomaly. The mean in the mountainous regions above 
the general level is about three and one-half times greater than the average new-method anomaly. 

From the above comparisons it must be realized that the Bouguer and free-air anomalies 
have decided relations to the topography, consequently the anomalies from these two methods 
of reduction are of much less value than the new-method anomalies for the purpose of deter¬ 
mining the distribution of materials in the earth’s crust and for other geodetic purposes. 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


17 


GRAPHICAL COMPARISON OF THE THREE KINDS OF ANOMALIES. 

A comparison of illustrations, Nos. 2, 3, and 4 at the end of this paper, will supplement 
the comparison of the three kinds of anomalies given on pages 12 to 15. One of the 
severest tests of a method of reduction is whether the positive and negative areas, as indicated 
by the signs of the anomalies, are nearly balanced in any extensive region under consideration. 
Illustrations Nos. 2, 3, and 4 show the areas of positive anomalies by the green shading and the 
negative areas by the yellow shading. Lines of equal anomalies, corresponding to contours on 
a topographic map, are drawn at intervals of 0.010 dyne or centimeter. t The contours are in 
black, and no distinction is made between the positive and negative contours. In constructing 
the contours each station was connected by straight lines with the stations nearest it in each 
direction. Interpolations were made along each of the lines to fix the points through which 
the lines of equal anomaly pass. The contours are to be considered somewhat generahzed. 
Illustration No. 2 shows the anomaly contours for the new method of reduction. The appear¬ 
ance of the map indicates that the areas of positive and negative anomalies are about equal 
in extent and that the grades as shown by the contours are not steep, except near Seattle. 
The positive areas form about 45 per cent of the whole area. There is no apparent connection 
between the contours on this illustration and the topography, except that the negative areas 
seem to predominate along the coasts. The negative anomalies at coast stations are, with few 
exceptions, very small and the geologic formation may be the cause of these. On pages 19 and 
20 it is shown that the anomalies in the Cenozoic formation tend slightly to be negative. 
The formation on the coast is largely Cenozoic. The anomalies in the large negative area at 
the left side of the illustration may be partly due to the effusive and intrusive formations, which, 
sa shown on pages 19 and 20, tend to have negative anomalies. Although about 40 per cent 
more stations are considered here than in Special Publication No. 10, yet the contours on a 
similar illustration in that publication agree remarkably well with those on illustration No. 2 
of this investigation. 

Illustration No. 3 shows the lines of equal anomalies for the Bouguer reduction. The pre¬ 
dominant characteristics of these contours are that nearly the whole area in the interior of the 
country is negative, the slopes are steep, and there is a decided relation between the topography 
and the size and sign of the anomalies. The low contours are in the areas with small elevations 
and the high contours are in the regions with great elevations. The sea-coast contours have 
a very decided tendency to be positive. The tendency of the Bouguer anomalies to be negative 
in the interior and positive on the coast is a characteristic of that method of reduction. Illus¬ 
tration No. 3 is in marked contrast to illustration No. 2, which shows the new-method anomaly 
contours. In the former only about 15 per cent of the total area is covered by positive contours. 

Owing to the use of the Helmert formula for Vienna in the first investigation and the change 
in the adopted value of gravity at Washington from 980.111 to 980.112, each of the Bouguer 
and free-air anomalies in Special Publication No. 10 differs from the anomalies in this report 
by —0.017 dyne. In other words, in that publication the positive anomalies are less and the 
negative anomalies are greater by 0.017 dyne than the Bouguer and free-air anomalies con¬ 
sidered here. The effect of the change from the formula of the Vienna system to that of the 
Potsdam system and the change of one thousandth of a dyne in the value of gravity for the 
base station is practically a change of datum for the Bouguer and free-air anomaly contour 
maps. The effect of this change of datum is scarcely noticeable on the Bouguer map. 

The free-air anomaly contours are shown on illustration No. 4. The positive area greatly 
predominates, only 25 per cent of the total area being negative. This is in great contrast to the 
Bouguer contours on illustration No. 3. A comparison of illustrations Nos. 2 and 4 shows that 
each negative area of the free-air anomaly map comes within a negative area of the new-method 
anomaly map. The difference between the two maps is principally in the different sizes of the 
negative areas. 


18 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


In several cases there were two stations close together with great differences in elevation. 
In each case the anomaly of the station with the elevation nearest the general elevation of the 
surrounding country was used for controlling the contours. 

An analysis of the three methods indicates clearly the cause of the principal characteristics 
of the three anomaly contour maps. By the Bouguer method the effect of the compensation 
is ignored and the computed gravity at a station in the interior is too great and on and near the 
coast the computed gravity is too small. Hence the anomaly contours will be negative in the 
interior and will tend to be positive at the coast. In the free-air reduction the resultant of the 
effect of the topography and its compensation is ignored, and the result is that in general the 
computed gravity is too small, and the anomalies have a marked tendency to be positive. The 
new method takes into account both the topography and the compensation and consequently 
the anomalies should not show any decided tendency to be of one sign and there should be no 
relation between the size and sign of the anomalies and the topography. An inspection of the 
new-method anomaly contour map shows that these conclusions are borne out by the facts. 

RELATION BETWEEN NEW-METHOD ANOMALIES AND AREAS OF EROSION AND DEPOSITION. 

It is reasonably certain that the erosion and deposition of material has an effect on the 
intensity of gravity, but no clear relation can be discovered between the new-method gravity 
anomalies and areas of erosion and deposition. At the mouths of rivers canying great 'quan¬ 
tities of materials one should expect gravity to be in excess. But in the United States the 
anomalies at stations near the mouths of large rivers have both signs. The fact that there is 
no definite relation between the new-method anomalies and areas of erosion and deposition 
indicates that the isostatic adjustment takes place soon after (geologically) the changes in the 
topography. 

RELATION BETWEEN THE NEW-METHOD ANOMALIES AND THE GEOLOGIC FORMATIONS. 

The following tables show the geologic formation in which each of the gravity stations is 
located. The 124 stations used in this investigation were platted on the geologic map of North 
America which bears the following title: “Geologic Map of Ncrth America, compiled by the 
United States Geological Survey, in cooperation with the Geological Survey of Canada and 
Instituto Geologico De Mexico, under the supervision of Bailey Willis and George W. Stose, 
Scale 1:5,000,000, 1911.” The decision as to the surface geologic formation on which the 
stations are located was based entirely on this map. It is probable that the classification would 
be slightly different if some other source of information were used. 1 The writer believes, how¬ 
ever, that only minor changes would be made in the tables given below and the conclusions 
drawn from them would not be materially changed. 

In the tables are given the stations and their new-method anomalies for each of the fol¬ 
lowing formations: (1) Archeozoic and Proterozoic, (2) Paleozoic, (3) Mesozoic, (4) Cenozoic, 
(5) Effusive, (6) Intrusive, (7) Unclassified. 

Stations and new-method anomalies for specified formations. 


ARCHEOZOIC AND PROTEROZOIC FORMATIONS. 


Station 

number 

New-method 
anomaly in 
dynes 

Station 

number 

New-method 
anomaly in 
dynes 

Station 

number 

New-method 
anomaly in 
dynes 

Station 

number 

New-method 
anomaly in 
dynes 

16 

+.015 

45 

+.020 

58 

+.023 

102 

+. 004 

24 

+.022 

57 

+.038 

75 

+.052 

107 

+. 024 

43 

+.021 



i • 




1 In the publication The Effect of Topography and Isostatic. Compensation upon the Intensity of Gravity the decision as to the geologic forma¬ 
tion on which the S9 stations there considered was based upon the geological map of North America bearing the following title: “Carte Geologique 
de L’Amgrique du Nord, Dressge d’apres les sources officelles des Etats Unis, du Canada, de la Rgpublique du Mexique, de la Co mmi ssion du 
Chemin de Fer Intercontinental, etc., Henry Gannett, Gdographe, et Bailey Willis, Ggologue, Eeheiie, 1:5,000,000,1906.” 

















EFFECT OF TOPOGRAPHY AND ISOSTATTC COMPENSATION ON GRAVITY. 


19 


Stations and new-method anomalies for specified formations —Cotinued. 

PALEOZOIC FORMATION. 


Station 

number 

New-method 
anomaly in 
dynes 

Station 

number 

New-method 
anomaly in 
dynes 

Station 

number 

New-method 
anomaly in 
dynes 

Station 

number 

New-method 
anomaly in 
dynes 

12 

-.027 

35 

-.009 

74 

+.059 

105 

-.021 % 

14 

+.026 

36 

-.007 

78 

+.002 

106 

-.013 

20 

+.010 

37 

-.005 

85 

+ .001 

119 

+ .015 

29 

+. 005 

38 

-. 005 

88 

-.010 

120 

-.008 

30 

+. 005 

39 

-.016 

89 

-.020 

121 

+ .002 

32 

-.023 

59 

+.019 

96 

-.052 

122 

+.011 

33 

-.003 

61 

-.029 

101 

+. 040 

123 

-.043 

34 

-. 019 

72 

+.032 

104 

-.024 

124 

-.033 


MESOZOIC FORMATION. 


10 

-.008 

42 

-.007 

60 

+.001 

77 

+.029 

11 

-.010 

46 

+. 024 

62 

+. 031 

91 

+.036 

23 

-.011 

47 

-.021 

70 

-.013 

94 

-.017 

25 

-. 019 

54 

-. 023 

71 

+. 003 

108 

-.006 

40 

+.014 

55 

-.003 

73 

+. 005 

118 

+.014 


CENOZOIC FORMATION. 


1 

+.008 

17 

-.021 

76 

+.002 

97 

-.011 

2 

+. 018 

18 

-.021 

79 

+. 008 

99 

-.016 

3 

+.010 

44 

-. 016 

80 

-.013 

100 

-.017 

4 

000 

53 

l i n qq 

82 

+.013 

109 

H-032 

5 

-.013 

56 


83 

-.006 

112 

+. 033 

6 

+. 016 

63 

+. 007 

90 

-. 048 

115 

-.009 

7 

-.009 

64 

-.050 

92 

+. 010 

117 

•’+■ 036 

8 

+. 027 

65 

+. 009 

93 

-.044 


9 

-.020 

66 

-. 050 

95 

+.001 




EFFUSIVE FORMATION. 


50 

-.002 

52 

-. 001 

98 

+. 021 

113 

-.027 

51 

+.021 

81 

-.010 

110 

-.015 

114 

-.028 


INTRUSIVE FORMATION. 


28 

-.020 

86 

+. 006 

103 

-.029 

111 

-.628 

31 

-.008 








UNCLASSIFIED. 


13 

+. 030 

22 

+.039 

48 

+. 004 

69 

-.010 

15- 

-.023 

26 

+.024 

49 

+.010 

84 

+.037 

19 

-.013 

27 

+.022 

67 

-.013 

87 • 

+.021 

21 

+.037 

41 

-.012 

68 

+.001 

116 

-.021 


1 Only one anomaly is used for the two Seattle stations. 

2 This station is only 14 miles from a pre-Cambrian formation. 

3 This station is only 6 miles from a pre-Cambrian formation. 


The unclassified stations are those which plot on the geologic map near the dividing line 
between two formations, or in a locality where there are several formations within a few miles 
of the station. 

The table shown below gives the means of the new-method anomalies with and without 
regard to sign and the number of stations in each of the several groups. 

















































































20 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


Summary. 


Geologic formation 

Number of stations 

Mean anomaly 

All 

With plus 
anomalies 

With minus 
anomalies 

With 
regard to 
sign 

Without 
regard to 
sign 

Archeozoic and Proterozoic 

9 

9 

0 

+0. 024 

0. 024 

Paleozoic 

32 

13 

19 

- .004 

. 019 

Mesozoic 

20 

9 

11 

+ . 001 

.015 

Cenozoic 

33 

15 

17 

- .007 

. 021 

Effusive 

8 

2 

6 

- .005 

.016- 

Intrusive 

5 

1 

4 

- .016 

. 018 

Unclassified 

16 

10 

6 

+ .008 

.020 

All stations 

123 

59 

63 

- .001 

.019 


One station in the Cenozoic formation has a zero anomaly. Only one anomaly was used 
for the two Seattle stations. Those stations are very near together, and the same very large 
anomaly, —0.093 dyne, is found at each. The introduction of the second anomaly would only 
have enlarged the means given in the table. 

The data shown in the above table are in substantial agreement with the table shown on 
page 114 of the Effect of Topography and Isostatic Compensation upon the Intensity of Gravity, 
Special Publication No. 10. * 

The mean of all the 123 anomalies with regard to sign is — 0.001 dyne and the mean without 
regard to sign is 0.019 dyne. These means each differ 0.001 from those given in the table on 
page —, owing to the introduction of the anomaly of —0.093 at one of the Seattle stations. It 
is evident from the above table that gravity is in excess and the topography under compensated 
at the stations in the Archeozoic and Proterozoic formations, for all of the nine anomalies 
are plus and the mean with regard to sign is +0.024. This is necessarily the average size of the 
anomaly without regard to sign, and it is considerably larger than the mean of the anomalies at 
all of the stations. There was one station, No. 15, at Atlanta, Ga., with a negative anomaly, 
which is on a narrow strip of old rock but this narrow strip runs through an extensive area of 
intrusive rock. As this station was within 2 miles of the intrusive rocks it was placed in the 
unclassified group. 

The most recent formation, the Cenozoic, has 33 stations, the anomalies of which are nearly 
equally divided as to sign, and the mean with regard to sign is —0.007 dyne. This would 
indicate that the topography in this formation is overcompensated and gravity is in defect. 
However, the very large anomaly at the Seattle station has a great influence on the size of the 
mean of this group and it will be well to consider the condition of the anomalies with this station 
omitted. If it is rejected, there will remain 32 stations in the Cenozoic formation, 15 with plus 
and 16 with minus anomalies and one with a zero anomaly. The mean with regard to sign 
will then be —0.004, which is very close to normal, and the mean without regard to sign will 
be 0.018, which is the average size of all the anomalies in the United States after rejecting the 
Seattle stations. 

The Paleozoic and Mesozoic formations which are of intermediate ages have 32 and 20 
stations respectively In each the minus anomalies are slightly more numerous than the plus 
anomalies. The Paleozoic anomalies have a mean of —0.004 with regard to sign and 0.019 
without regard to sign. The Mesozoic anomalies have a mean with regard to sign of +0.001 
and without regard to sign the mean is only 0.015. 

There are 8 stations in the Effusive formation and 6 have minus anomalies. The mean 
with regard to sign is —0.005, which indicates that gravity is somewhat in defect and the 
topography overcompensated. The largest anomaly in this formation is only 0.028. There 
are only 5 stations in the Intrusive formation and 4 of them have negative anomalies. The 
one anomaly with the positive sign is only +0.006. The mean of the five anomalies with regard 





















EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


21 


to sign is —0.016, which shows that the gravity is very much in defect and the topography 
largely overcompensated. The largest anomaly in this formation is 0.029. If the Intrusive 
and Effusive anomalies were combined into one group then the mean with and without regard 
to sign would be —0.009 and 0.017 respectively. 

Of the 14 plus anomalies of 0.030 or greater, 2 are in the Archeozoic and Proterozoic group, 
3 in the Paleozoic, 2 in the Mesozoic, 3 in the Cenozoic and 4 in the Unclassified. There are 
9 negative anomalies of 0.030 or larger. Of these 3 are in the Paleozoic and 6 in the Cenozoic. 
There is no anomaly as great as ±0.030 in the Effusive or Intrusive formations. 

In general the rocks of the oldest formations have greater densities than 2.67, the adopted 
mean value for the surface density of the earth, and this fact may lead one to conclude that 
the gravity should be greater on these formations. But it will appear on reflection that these 
can not be merely surface phenomena. 

Let it be assumed that the pressure at the depth of 113.7 kilometers under a station of the 
oldest formations is normal (that is, the crust is in a state of perfect isostasy) and let it be 
assumed that the average anomaly with regard to sign of +0.024 is caused by an erroneous 
assumption regarding the surface density. Then if the formation considered extends 19 kilo¬ 
meters in every direction from the station and to a depth of 1000 feet, an increase in density of 
2.06 would be necessary to cause an anomaly of +0.024. With the same radius but a depth 
of 10 000 feet the necessary increase of density would be 0.20. 

The maximum anomaly in the oldest formation is +0.052 and this could be caused by an 
increase in density of 0.43 in a disk of material about the station with a radius of 19 kilometers 
and a depth of 10 000 feet. 

With the depth of 10 000 feet and a radius of 19 kilometers in the geologic formation 
at a station, the average anomaly of —0.016 in the Intrusive group could be caused by a change 
in density of —0.13. 

To cause the maximum negative anomaly of —0.093, at Seattle, would require a decrease 
of density of 0.82 in the material of a disk 10 000 feet thick and a radius of 19 kilometers 
directly under the station. 

A more reliable geologic map and 35 more gravity stations were used in this investigation 
than in the first one, but the data in the above table are in general in close agreement with 
those shown in the table on page 114 of the report on the first investigation. They differ in 
regard to the Intrusive and Effusive formations the anomalies of which in the first investi¬ 
gation have a mean with regard to sign that is about normal, while in this investigation the 
anomalies have a strong tendency to be negative. Also the anomalies of the Cenozoic forma¬ 
tion in the present investigation have a mean with regard to sign of only —0.007, while in the 
first investigation it was —0.011 dyne. The second investigation shows that the mean with 
regard to sign at stations in the oldest formations is somewhat greater than in the first inves¬ 
tigation. The data from the two investigations for the Paleozoic and Mesozoic formations 
agree very closely. 

From the considerations stated above it seems probable that the excesses and deficiencies 
of mass which cause the largest of the anomalies can not be surface phenomena alone and 
that such excesses and defects must extend through depths at least as great as 15 000 feet. 
There is no conclusive evidence from gravity observations to indicate whether the anomalies 
of the average size are caused by difference between the actual and the assumed density of the 
earth’s surface material near the station or whether such anomalies are caused by an actual 
departure from a state of complete isostasy. 

NEW-METHOD ANOMALIES IN AGREEMENT WITH DEFLECTIONS-OF-THE-VERTICAL RESIDUALS. 

Illustration No. 5. shows the residuals of solution H of the Supplemental Investigation 
in 1909 of the Figure of the Earth and Isostasy, and the gravity stations with their new- 
method anomalies. The deflections indicated that there was an excess of mass in some areas 
and a defect of mass in others. These areas are shown by red lines on this illustration. In 


22 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


only one or two cases was the gravity known before the outlines of the areas were drawn. 
Since the publication of the Supplemental Investigation in 1909 of the Figure of the Earth 
and Isostasy, in which this illustration first appeared, at least one gravity station was estab¬ 
lished in or very near each of the areas inclosed by red lines except the areas near Chester, Ill., 
and near the Santa Barbara Channel, Cal. In no case did the sign, as indicated by the deflec¬ 
tion residuals, differ from the sign of the new-method anomalies of the gravity stations. Wher¬ 
ever the gravity stations are near the astronomic stations there is no important conflict between 
the evidence furnished by the deflections and the gravity stations as to the location of areas 
of excessive and defective density. It is possible that an investigation based upon a combina¬ 
tion of deflection and gravity stations may furnish means to determine approximately the 
location with respect to depth of the excesses and deficiencies of mass. 

REGIONAL VERSUS LOCAL DISTRIBUTION OF COMPENSATION. 

On pages 98 to 102 of the "Effect of Topography and Isostatic Compensation upon the 
Intensity of Gravity” there was a discussion under the above heading. The anomalies were 
computed with regional distribution of the compensation within the outer limits of zones K, 
M, and O (radii of 18.8, 58.8, and 166.7 kilometers, respectively). The evidence for the first 
investigation was from only 44 stations in the United States and 4 foreign stations. These 
data are now supplemented by similar data for all the remaining stations in the United States. 
The average anomaly with regard to sign by the new method with local compensation, and 
the average anomaly by each of the three new-method reductions with regional distribution 
of the compensation are repsectively —0.002, —0.001, —0.001, and —0.002 dyne. The means 
without regard to sign for the different distributions of the compensation are respectively, 
0.020, 0.019, 0.019 and 0.020 dyne. These mean anomalies give only negative evidence. 

There are 22 stations in the United States in mountainous regions and below the general 
level and the means, with regard to sign, of the anomalies by the four methods of distribution 
are 0.000, +0.001, +0.003, and +0.005 dyne, while the means without regard to sign are 
respectively 0.017, 0.017, 0.018, and 0.019 dyne. For the 18 stations in the United States in 
mountainous regions and above the general level the means, with regard to sign, of the anomalies 
by the several methods of distribution of the compensation are +0.003, +0.003, 0.000, and 
— 0.010 dyne. The means without regard to sign, are respectively 0.018, 0.018, 0.017, and 0.020 
dyne. 

The mean, with regard to sign, of the anomalies for the stations at each of the two moun¬ 
tain groups, indicates that the theory of regional distribution of compensation to the outer 
limit of zone O, 166.7 kilometers, is far from the truth. So far as may be judged from the other 
average anomalies no one method seems to have any decided advantage. (See pp. 98-102 of 
Special Publication No. 10.) 

PERCENTAGE OF COMPLETENESS OF COMPENSATION. 

On page 111 of Special Publication No. 10 it was shown that the gravity anomaly may be 
interpreted in terms of excess or deficiency of masses of known extent. As a mean working 
hypothesis it was assumed that ordinarily 0.0030 dyne of anomaly is due to an excess or defi¬ 
ciency of mass equivalent to a stratum 100 feet thick. This wor kin g hypothesis is equivalent 
either to the assumption that excess (or deficiency) of mass is uniformly distributed to a depth 
of 113.7 kilometers and extends to a distance of 166.7 kilometers and less than 1190 kilometers 
from the station, or to the assumption that it extends to a distance of 166.7 kilometers from the 
station and is distributed to an effective mean depth of more than 15 000 feet and less than 113.7 
kilometers, or the working hypothesis may be considered to be a combination of the two 
assumptions. 

From the evidence given by deflections of the vertical the conclusion has been drawn that 
in the United States the average departure from complete compensation corresponds to excesses 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


23 


or deficiencies of mass represented by a stratum only 250 feet thick on an average. 1 2 The 
gravity determinations indicate this average to be 630 feet instead of 250 feet. In neither 
case is the average value determined or defined with a high grade of accuracy. The difference 
between the two determinations of the average value is therefore of little importance. The 
determination given by the gravity observations is probably the more reliable of the two. 
Each determination is significant mainly as showing that the isostatic compensation is nearly 
perfect. 

The average elevation in the United States above mean sea level is about 2,500 feet. There¬ 
fore, from gravity observations alone the compensation may be considered to be about 75 per 
cent complete on an average for stations in the United States. 

DEPTH OF COMPENSATION. 

No tests of the depth of compensation from the anomalies have been made except for 10 
stations, for which data are given on page 105 of Special Publication No. 10. It is hoped to make 
a test in the near future of the depth of compensation with the new-method gravity anomalies 
at all stations in the United States. 


ALASKA GRAVITY STATIONS. 


There are shown in the table given below the principal facts for 10 stations in Alaska 3 
established by the Coast and Geodetic Survey. Only the stations at St. Paul Island in 1891, 
at St. Michael in 1898, and at Fort Egbert in 1905 can be considered primary in character. The 
other stations were established incidentally to other field work, and the determination of the 
chronometer corrections was weak. At all of the stations the half-second pendulums were used. 
It is difficult to obtain a definite idea as to the accuracy of the derived value of the intensity 
of gravity at the stations other than St. Paul, St. Michael, and Fort Egbert. The writer believes, 
however, that the value of the intensity of gravity at each of the secondary stations may be 
uncertain by as much as 0.020 dynes. 


Name of station 



1 


H 

Yo 

Correction 

for 

elevation 

Correction 

for 

topography 
and com¬ 
pensation 

Computed 
gravity at 
station ( g c ) 

Observed 
gravity at 
station ( g ) 

( g-gc ) 

Fort Egbert, Eagle City 

64 

47.4 

141 

12.4 

Meters 

269 

982.271 

-0.083 

-0.042 

982.146 

982.183 

+0.037 

Juneau 

58 

17.5 

134 

24 

5 

981.778 

- .002 

- .075 

981. 701 

981.744 

+ .043 

Yakutat Bay 

59 

33.8 

139 

47.3 

4 

981.880 

- .001 

- .018 

981. 861 

981.835 

- .026 

Pyramid Harbor 

59 

11.8 

135 

26.8 

5 

981.850 

- .002 

- .086 

981. 762 

981.822 

+ .060 

Sitka 

57 

02.9 

135 

20.4 

9 

981. 676 

- .003 

+ .007 

981.680 

981. 694 

+ .014 

Wrangell 

56 

28.3 

132 

23.2 

7 

981.628 

- .002 

- .047 

981.579 

981. 6C3 

+ .024 

Burroughs Bay 

56 

02.2 

131 

06.1 

0 

981.591 

.000 

- .067 

981. 524 

981.507 

- .017 

St. Paul Island 

57 

07.3 

170 

16.6 

10 

981. 6S2 

- .003 

+ .041 

981.720 

981.726 

+ .006 

St. Michael 

63 

28.5 

162 

02.4 

1 

982.178 

.000 

- .004 

982.174 

982.192 

+ .018 

Port Simpson, British Columbia 

54 

33.6 

130 

25.5 

6 

981. 466 

- .002 

- .029 

981.435 

981. 464 

+ .029 


In the following table there are given the anomalies at the Alaska stations for the three 
methods of reduction. The anomalies for the two older methods were copied from Verhand- 
lungen, Sechzehnten Allgemeinen Conferenz, Internationalen Erdmessung, III Teil, Berlin, 
1911, except in the case of Fort Egbert. After this place was connected with the seacoast by 
precise leveling the elevation used for the gravity station was changed from 174 meters to 269 
meters. The change in elevation will account for the difference in the anomalies at Fort Egbert 
from those given in the above publication. 


1 The Figure of the Earth and Isostasy, etc., pp. 164-166, and Supplementary Investigation in 1909 of the Figure of the Earth and Isostasy, p. 59. 

2 One of these stations at Port Simpson is really in Canadian territory, near the extreme portion of southeastern Alaska. 
















24 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


Name of station 

Anomaly 

New method 

ff-' (^c+0.008) 

Bouguer 
( g"o—ro ) 

In free air 
(ffo—ro) 

Fort Egbert, Eagle City 

Juneau 

Yakutat Bay 

Pyramid Harbor 

Sitka 

Wrangell 

Burroughs Bay 

St. Paul Island 

St. Michael 

Port Simpson, British Columbia 

+0. 029 
+ .035 

- .034 
+ .052 
+ .006 
+ .016 

- .025 

- .002 
+ . 010 
+ .021 

-0. 031 

- .033 

- .044 

- .027 
+ .020 

- .024 
- .084 

+ .046 
+ .014 

- .001 

-0. 005 

- . 032 

- .044 

- .026 
+ .021 
- .023 

■ .084 
+ .047 
+ .014 
.000 


Owing to the small number of stations in Alaska and the fact that 7 of the 10 stations are 
not primary in character, it will not serve any useful purpose to discuss them as a group. The 
data for these stations are inserted in this paper for use in getting a value for the flattening of 
the earth. (See p. 23.) It is hoped that a number of primary gravity stations may be estab¬ 
lished in Alaska in the not distant future. 

FLATTENING OF THE EARTH. 

In the writer’s opinion the severest test to which the new method can be subjected is a 
determination of the flattening of the earth from the stations in the United States, which are 
few in number and limited in range of latitude as compared with those used by Helmert in 
deducing his flattening, 1/298.3. 

The stations in the United States were arranged in groups according to latitude. (In 
these tests the two Seattle stations were rejected.) The zones selected for the groups were four 
degrees wide, with middle latitudes of 27°, 31°, 35°. 39°, 43°, and 47°, respectively. The Hel¬ 
mert formula of 1901, j 0 = 978.030(1 + 0.005302sin 2 </>—0.000007sin 2 2</>),was used as a basis of 
the computations, and the anomaly at each station was given unit weight, except that where 
there was a group of two or more stations located close together the mean anomaly for the group 
was used. This mean anomaly for a group was also given unit weight. The mean anomalies 
for the stations in the several zones selected were assumed to have been due entirety to erro¬ 
neous values of the coefficients in the Helmert formula. 

The coefficient 0.000007 was assumed to be correct. 

The general form of observation equation is: 

0 = ty 0 — g 0 ) + (1+0.005302 sin 2 </> —0.000007 sw 2 2cf>)X 1 + 978.030 sin 2 cf>X 2 . 

f 0 is the computed value of gravity as given by Helmert’s formula. g 0 is the corresponding 
observed value reduced to sea level and corrected for topograplry and isostatic compensation. 
jo — g 0 is, therefore, the new-methad anomaly with reversed sign. X t is the correction to 
978.030, and X 2 is the correction to 0.005302. 

In the following table there are given for each zone the number of anomalies and the 
average new-method anomaly. As stated above, the mean anomaly was taken where two or 
more stations were close together. 


Number of 
anomalies 

Middle lati¬ 
tude of zone 

Anomaly, new 
method 

Number of 
anomalies 

Middle lati¬ 
tude of zone 

Anomaly, new 
method 

5 

27° 

+ 0 . 017 

29 

39° 

+ 0 . 001 

15 

31° 

+ 0 . 002 

28 

43° 

+ 0 . 012 

21 

35° 

+0. 003 

16 

47 ° 

+ 0 . 011 


















EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


25 


The observation equations are: 

0= -0.017 + 1.0011X^201.6X3 
0= - 0.002+ i.ooi4X 1 +259.4X3 
0= -0*.003 + 1.0017X 1 +321.8X3 
0= -0.004 + 1.002lXj + 387.5X 2 
0 = - 0.012 +1.0025Xj + 455.0X3 
0- - 0.011 + 1.0028X 1 + 523.lX 2 

The normal equations are: 

0 = - 0.04910 + 6.0232Xj + 2152.95X 2 
0 = - 17.6755 + 2152.95X t + 842301.0X,. 

The solution gives: 

X x = +0.00753 
X 2 = +0.00000174. 

The resulting formula for the theoretical value of gravity at sea level is: 

To = 978.038(1+0.005304 sin 2 <£-0.000007 sin 2 2 <f>). 

+ 6 ±17 

The derived reciprocal of the flattening is 298.4 + 1.5, which agrees almost exactly with 
the Helmert value, 298.3+0.7, as derived from a great many gravity stations having a great 
range in latitude. The probable errors of the terms in the new formula are large and are prob¬ 
ably due to the very large mean positive anomaly for latitude 27°. In the table above it 
will be seen that there are only five stations in this group. 

On page 10 a correction of +0.008 was applied to the first term of Helmert’s formula. 
This was the mean anomaly with regard to sign for 122 gravity stations in the United States 
(Seattle stations omitted). The above formula derived from the stations in the United States 
shows that the application of this correction was justified. The writer does not believe that it 
would be advisable to change the second term of Helmert’s formula as the new value for the 
second term has not the precision of the new value for the first term. 

In order to test the reliability of this value of the reciprocal of the flattening from all 
stations in the United States the stations were divided into two groups, those east of the ninety- 
seventh meridian of longitude and those west of that meridian. 

With 62 anomalies east of longitude 97° the theoretical formula is: 

y 0 = 978.040(1+0.005297 sin 2 0-0.000007 sin 2 2^>). 

±8 ±20 

and the resulting reciprocal of the flattening is 297.8 + 1.8. 

For the 52 anomalies to the west of longitude 97° the theoretical formula is: 

7" o = 978.032(l +0.005319 sin 2 <£- 0.000007 sin 2 2<rS). 

±8 ±21 

and the derived reciprocal of the flattening is 299.6 + 1.9. 

These values of the reciprocal of the flattening are in such close agreement with the best 
values derived from great numbers of gravity observations and deflections of the vertical that 
it is believed that the results prove that the new method of reduction is very close to the truth 
and that the area of the United States is in a state of nearly perfect isostatic equilibrium. 

A further test was made by combining the anomalies at the 10 Alaska stations with those 
in the United States. The resulting theoretical formula is: 

To = 978.030(1 +0.005326 sin 2 <£- 0.000007 sin 2 2<£). 

±4 ±8 

and the derived reciprocal of the flattening is 300.4 + 0.7. 

Owing to the secondary character of 7 of the 10 Alaska gravity stations the mean anomalies 
for the two 5-degree zones used, with middle latitudes 56° 30' and 61° 30', may be largely in 


26 


EFFECT OF TOPOGRAPHY AND ISOSTATIC COMPENSATION ON GRAVITY. 


error from the observations alone. Also the topographic maps used in reducing the Alaska 
stations were not very accurate and the errors from this source may be some thousandths of a 
dyne. However, the reciprocal of the flattening from the combination of the United States and 
Alaska stations is close to those derived from the stations in the United States alone. 

The close agreement of the above four values of the reciprocal of the flattening of the earth 
from the new method of reduction can not be fully appreciated until they are compared with 
the values derived from the anomalies by the older methods of reduction. 

By following the same method of computation as that used for the new method and using 
122 stations in the United States (omitting the Seattle stations) the theoretical formula 
resulting from the free-air method is: 

To = 978.072(1+0.005232 sin 2 ^-0.000007 sin 2 2^>). 

±7 ±19 

The deduced reciprocal of the flattening is 292.1 ±1.7. 

The reciprocal of the flattening for the stations in the eastern half of the United States 
from this method is 292.4±3.0, for the western half of the United States it is 294.3±2.8, and 
for the combination of the Alaska stations and those in the United States the reciprocal of 
the flattening is 291.2±0.7. 

Similarly the theoretical formula resulting from the Bouguer method of reduction, using 
the 122 stations in the United States, is: 

\ 7-0 = 978.070 (1 + 0.005092 sin 2 ^ - 0.000007 sin 2 2<j b) 

±31 ±82 

and the derived reciprocal of the flattening is 280.7 ±7.2. 

The reciprocal of the flattening for the stations in the eastern half of the United States 
from the Bouguermethod is 284.9±3.3, for the western half of the United States it is 279.1 ± 12.5, 
and for the combination of the stations in Alaska and the United States it is 296.1 ±4.1. 

The following table gives the reciprocal of the flattening for each of the three methods of 
reduction for each of the four groups of stations considered: 


Summary <>j values of reciprocal oj the flattening. 



New method 

Free air 

Bouguer 

All stations in the United States 

298. 4±1. 5 

292 1±1. 7 

280. 7-t- 7. 2 

Stations in eastern half of United States 

297. 8 - 1 -I. 8 

292. 4-4-3. 0 

284. 9-4- 3. 3 

Stations in western half of United States 
Combination of stations in Alaska and the United 

299. 6±1. 9 

294. 3±2. 8 

279.1±12. 5 

States 

300. 4±0. 7 

291. 2±0. 7 

296.1± 4.1 


It is seen that the values of the flattening derived from the older methods of reductions 
are far from the truth (except the last Bouguer value shown), and it is apparent that no reliable 
values can be obtained from those methods with limited numbers of stations in a small range 
of latitude. In contrast the values from a small number of stations reduced by the new method 
and with a small range of latitude are very near the truth. 

It is the writer's belief that if all the available gravity stations of the world were reduced 
by the new method of reduction a theoretical formula for gravity at sea level and a value of 
the flattening of the earth could be obtained which would have very great precision, and be 
extremely close to the truth. 

SUMMARY. 

The second or supplementary investigation of the Effect of Topography and Isostatic 
Compensation upon the Intensity of Gravity, of which this paper is a report, gives results which 
agree in every important particular with the results of the first investigation which are pub- 



















EFFECT OF TOPOGRAPHY AND ISOSTATTC COMPENSATION ON GRAVITY. 


27 


lished in the United States Coast and Geodetic Survey publication entitled “Effect of Topog¬ 
raphy and Isostatic Compensation upon the Intensity of Gravity, Special Publication No. 10,” 
by J. F. Hayford and William Bowie. 

In the first investigation the Helmert formula in the Vienna system was used for com¬ 
puting the theoretical value of gravity at sea level. The stations in the United States are in 
the Potsdam system, and thus an error was made in the theoretical gravity at sea level for 
each station. This did not affect the new-method anomalies, for, before computing them, a 
correction was applied to the first term of Helmert’s formula. This correction was equal to 
the mean with regard to sign of the difference between the observed and computed values of 
gravity at each station in the United States. The result of the use of the wrong formula on 
the Bouguer and free-air anomalies was to apply —0.016 dyne to each. In the supplementary 
investigation the Helmert formula in the Potsdam system has been used and the anomalies by 
each method of reduction are not subject to the above errors. The effect on the anomalies 
by the older methods of reduction may be clearly seen by comparing the means with regard 
to sign for the several groups of stations arranged according to the topography shown on 
pages 14 to 15 of this paper and on pages 77 to 78 of the Effect of Topography and Isostatic 
Compensation upon the Intensity of Gravity. The effects will be seen graphically by a compar¬ 
ison of illustrations Nos. 3 and 4 of this paper with illustrations Nos. 17 and 18 of the other 
publication. 

The more recent geological map used in this investigation gave a different geologic forma¬ 
tion around some of the stations from that stated in the first investigation. The mean anomalies 
with regard to sign are nearly zero for the stations in the Mesozoic and Paleozoic formations. 
If the two Seattle stations are not considered then the other 32 stations in the Cenozoic formation 
will have a mean anomaly with regard to sign of —0.004, which is very nearly normal. The 
anomalies at each of the 9 stations in the oldest formations are positive with a mean of +0.024. 
This indicates an excess of mass in the crust of the earth under these formations (p. 20). 
Of the anomalies at stations in Effusive and Intrusive formations 10 are negative and only 3 
positive. The mean with regard to sign for these anomalies is — 0.009 which indicates that 
there is in general a defect of mass in the earth’s crust under these formations (p. 20). 

It is probable that the causes of the anomalies are not merely surface phenomena. The 
average anomaly can not be accounted for by any reasonable assumption as to regional distri¬ 
bution of compensation (p. 22) nor by a horizontal displacement of the compensation (p. 
121 of the Effect of Topography and Isostatic Compensation upon the Intensity of Gravity.) 
Neither is it possible to account for the anomalies by any reasonable difference in the depth 
of compensation (p. 105 Special Publication No. 10). They are probably due in part to errors 
of observation and computation, to erroneous values in the assumed density of the materials 
of the upper portion of the earth’s crust near the station, and variations in the manner of distri¬ 
bution of the compensation with respect to depth (p. 22). The writer believes, however, 
that the principal cause of the larger anomalies is an actual departure from the state of perfect 
isostasy in the vicinity of the stations. 

It is the writer’s belief that the principal causes of the larger new-method anomalies are 
located within restricted areas surrounding the stations. This is clearly indicated graphically 
on illustration No. 2, which shows the stations and their new-method anomalies and the gravity 
contours. Particular notice should be given the change in anomaly from —0.020 at station 9 
to +0.027 at station 8 in a distance of only 280 kilometers; the change from —0.093 at stations 
53 and 56 to +0.033 at station 112, in a distance of only 90 kilometers; the change from —0.021 
at station 47 to +0.024 at station 46, a distance of only 140 kilometers; and the change from 
+ 0.037 at station 21 to —0.011 at station 23, in a distance of only 62 kilometers. There are 
numerous other pairs of stations which show large changes in the anomalies in comparatively 
short distances. This change in the anomalies at stations near each other is not confined to any 
particular type of topography. 

Four groups of gravity stations were used for determining the flattening of the earth. 
The new method of reduction gave values which ranged from 1/297.8 to 1/300.4 (p. 26) and 








ILLUSTRATION NO.I — Map Showing Location of Gravity Stat,o Ns usED in the investigation. 








































































































































































































































































































































































































































































































































































+.019 




+.008 Oy ni «e 


[isor® 3 7 


f®o«o» r 


>U»n*h u ® 


jnsK^oi 


Sprmgfn 


iFrauVfoi 




Saui tt p f 


El Reno 


73+005* 




:t Worth 


I acknon 


,T«uW h **j 


98^ 

+.0210 


US. Coast and Geodetic Survey 


0.H.Tittmann. Superintendent 


BASE MAP 0E THE UNITED STATES 


(Projected on intersecting cone) 


Scale I ; 7000000 


Positive areas 


Kilometers 


Went froto Crveowich 


1 Hf NORRIS PI TCRS CO.. WASHINGTON . D. 


ILLUSTRATION No. 2.— Lines of Equal Anomaly for New Method of Reduction 















































































































































































































































































































































































































































































































































































ILLUSTRATION No. 3 . — Lines of Equal Anomaly for bouguer Method of Reduction. 


THC NORRIS RfTFRS CO.. WASHINGTON 






























































































































































































































































































































































































































































































































































































ILLUSTRATION No. 4 . — Lines of Equal Anomaly for Free-Air Method of Reduction 















































































































































































































































































































































































































































































































































































































80 ° 



ILLUSTRATION No. 5.— Illustration from Supplementary Investigation in 1909 of the Figure of the Earth and Isostasy, Showing Residuals of Solution H, All Stations, with Areas of Excessive and Defective Density, and Showing also all Gravity Stations with New-Method Anomalies 































































































































































































































































































































































































































































































































































































































































































































































































